basic frame

diffusion/__init__.py

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+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+from . import gaussian_diffusion as gd
+from .respace import SpacedDiffusion, space_timesteps
+
+
+def create_diffusion(
+    timestep_respacing,
+    noise_schedule="linear", 
+    use_kl=False,
+    sigma_small=False,
+    predict_xstart=False,
+    learn_sigma=True,
+    rescale_learned_sigmas=False,
+    diffusion_steps=1000
+):
+    betas = gd.get_named_beta_schedule(noise_schedule, diffusion_steps)
+    if use_kl:
+        loss_type = gd.LossType.RESCALED_KL
+    elif rescale_learned_sigmas:
+        loss_type = gd.LossType.RESCALED_MSE
+    else:
+        loss_type = gd.LossType.MSE
+    if timestep_respacing is None or timestep_respacing == "":
+        timestep_respacing = [diffusion_steps]
+    return SpacedDiffusion(
+        use_timesteps=space_timesteps(diffusion_steps, timestep_respacing),
+        betas=betas,
+        model_mean_type=(
+            gd.ModelMeanType.EPSILON if not predict_xstart else gd.ModelMeanType.START_X
+        ),
+        model_var_type=(
+            (
+                gd.ModelVarType.FIXED_LARGE
+                if not sigma_small
+                else gd.ModelVarType.FIXED_SMALL
+            )
+            if not learn_sigma
+            else gd.ModelVarType.LEARNED_RANGE
+        ),
+        loss_type=loss_type
+        # rescale_timesteps=rescale_timesteps,
+    )

diffusion/diffusion_utils.py

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+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+import torch as th
+import numpy as np
+
+
+def normal_kl(mean1, logvar1, mean2, logvar2):
+    """
+    Compute the KL divergence between two gaussians.
+    Shapes are automatically broadcasted, so batches can be compared to
+    scalars, among other use cases.
+    """
+    tensor = None
+    for obj in (mean1, logvar1, mean2, logvar2):
+        if isinstance(obj, th.Tensor):
+            tensor = obj
+            break
+    assert tensor is not None, "at least one argument must be a Tensor"
+
+    # Force variances to be Tensors. Broadcasting helps convert scalars to
+    # Tensors, but it does not work for th.exp().
+    logvar1, logvar2 = [
+        x if isinstance(x, th.Tensor) else th.tensor(x).to(tensor)
+        for x in (logvar1, logvar2)
+    ]
+
+    return 0.5 * (
+        -1.0
+        + logvar2
+        - logvar1
+        + th.exp(logvar1 - logvar2)
+        + ((mean1 - mean2) ** 2) * th.exp(-logvar2)
+    )
+
+
+def approx_standard_normal_cdf(x):
+    """
+    A fast approximation of the cumulative distribution function of the
+    standard normal.
+    """
+    return 0.5 * (1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3))))
+
+
+def continuous_gaussian_log_likelihood(x, *, means, log_scales):
+    """
+    Compute the log-likelihood of a continuous Gaussian distribution.
+    :param x: the targets
+    :param means: the Gaussian mean Tensor.
+    :param log_scales: the Gaussian log stddev Tensor.
+    :return: a tensor like x of log probabilities (in nats).
+    """
+    centered_x = x - means
+    inv_stdv = th.exp(-log_scales)
+    normalized_x = centered_x * inv_stdv
+    log_probs = th.distributions.Normal(th.zeros_like(x), th.ones_like(x)).log_prob(normalized_x)
+    return log_probs
+
+
+def discretized_gaussian_log_likelihood(x, *, means, log_scales):
+    """
+    Compute the log-likelihood of a Gaussian distribution discretizing to a
+    given image.
+    :param x: the target images. It is assumed that this was uint8 values,
+              rescaled to the range [-1, 1].
+    :param means: the Gaussian mean Tensor.
+    :param log_scales: the Gaussian log stddev Tensor.
+    :return: a tensor like x of log probabilities (in nats).
+    """
+    assert x.shape == means.shape == log_scales.shape
+    centered_x = x - means
+    inv_stdv = th.exp(-log_scales)
+    plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
+    cdf_plus = approx_standard_normal_cdf(plus_in)
+    min_in = inv_stdv * (centered_x - 1.0 / 255.0)
+    cdf_min = approx_standard_normal_cdf(min_in)
+    log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
+    log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
+    cdf_delta = cdf_plus - cdf_min
+    log_probs = th.where(
+        x < -0.999,
+        log_cdf_plus,
+        th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))),
+    )
+    assert log_probs.shape == x.shape
+    return log_probs

diffusion/gaussian_diffusion.py

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+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+
+import math
+
+import numpy as np
+import torch as th
+import enum
+
+from .diffusion_utils import discretized_gaussian_log_likelihood, normal_kl
+
+
+def mean_flat(tensor):
+    """
+    Take the mean over all non-batch dimensions.
+    """
+    return tensor.mean(dim=list(range(1, len(tensor.shape))))
+
+
+class ModelMeanType(enum.Enum):
+    """
+    Which type of output the model predicts.
+    """
+
+    PREVIOUS_X = enum.auto()  # the model predicts x_{t-1}
+    START_X = enum.auto()  # the model predicts x_0
+    EPSILON = enum.auto()  # the model predicts epsilon
+
+
+class ModelVarType(enum.Enum):
+    """
+    What is used as the model's output variance.
+    The LEARNED_RANGE option has been added to allow the model to predict
+    values between FIXED_SMALL and FIXED_LARGE, making its job easier.
+    """
+
+    LEARNED = enum.auto()
+    FIXED_SMALL = enum.auto()
+    FIXED_LARGE = enum.auto()
+    LEARNED_RANGE = enum.auto()
+
+
+class LossType(enum.Enum):
+    MSE = enum.auto()  # use raw MSE loss (and KL when learning variances)
+    RESCALED_MSE = (
+        enum.auto()
+    )  # use raw MSE loss (with RESCALED_KL when learning variances)
+    KL = enum.auto()  # use the variational lower-bound
+    RESCALED_KL = enum.auto()  # like KL, but rescale to estimate the full VLB
+
+    def is_vb(self):
+        return self == LossType.KL or self == LossType.RESCALED_KL
+
+
+def _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, warmup_frac):
+    betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64)
+    warmup_time = int(num_diffusion_timesteps * warmup_frac)
+    betas[:warmup_time] = np.linspace(beta_start, beta_end, warmup_time, dtype=np.float64)
+    return betas
+
+
+def get_beta_schedule(beta_schedule, *, beta_start, beta_end, num_diffusion_timesteps):
+    """
+    This is the deprecated API for creating beta schedules.
+    See get_named_beta_schedule() for the new library of schedules.
+    """
+    if beta_schedule == "quad":
+        betas = (
+            np.linspace(
+                beta_start ** 0.5,
+                beta_end ** 0.5,
+                num_diffusion_timesteps,
+                dtype=np.float64,
+            )
+            ** 2
+        )
+    elif beta_schedule == "linear":
+        betas = np.linspace(beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64)
+    elif beta_schedule == "warmup10":
+        betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.1)
+    elif beta_schedule == "warmup50":
+        betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.5)
+    elif beta_schedule == "const":
+        betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64)
+    elif beta_schedule == "jsd":  # 1/T, 1/(T-1), 1/(T-2), ..., 1
+        betas = 1.0 / np.linspace(
+            num_diffusion_timesteps, 1, num_diffusion_timesteps, dtype=np.float64
+        )
+    else:
+        raise NotImplementedError(beta_schedule)
+    assert betas.shape == (num_diffusion_timesteps,)
+    return betas
+
+
+def get_named_beta_schedule(schedule_name, num_diffusion_timesteps):
+    """
+    Get a pre-defined beta schedule for the given name.
+    The beta schedule library consists of beta schedules which remain similar
+    in the limit of num_diffusion_timesteps.
+    Beta schedules may be added, but should not be removed or changed once
+    they are committed to maintain backwards compatibility.
+    """
+    if schedule_name == "linear":
+        # Linear schedule from Ho et al, extended to work for any number of
+        # diffusion steps.
+        scale = 1000 / num_diffusion_timesteps
+        return get_beta_schedule(
+            "linear",
+            beta_start=scale * 0.0001,
+            beta_end=scale * 0.02,
+            num_diffusion_timesteps=num_diffusion_timesteps,
+        )
+    elif schedule_name == "squaredcos_cap_v2":
+        return betas_for_alpha_bar(
+            num_diffusion_timesteps,
+            lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2,
+        )
+    else:
+        raise NotImplementedError(f"unknown beta schedule: {schedule_name}")
+
+
+def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):
+    """
+    Create a beta schedule that discretizes the given alpha_t_bar function,
+    which defines the cumulative product of (1-beta) over time from t = [0,1].
+    :param num_diffusion_timesteps: the number of betas to produce.
+    :param alpha_bar: a lambda that takes an argument t from 0 to 1 and
+                      produces the cumulative product of (1-beta) up to that
+                      part of the diffusion process.
+    :param max_beta: the maximum beta to use; use values lower than 1 to
+                     prevent singularities.
+    """
+    betas = []
+    for i in range(num_diffusion_timesteps):
+        t1 = i / num_diffusion_timesteps
+        t2 = (i + 1) / num_diffusion_timesteps
+        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
+    return np.array(betas)
+
+
+class GaussianDiffusion:
+    """
+    Utilities for training and sampling diffusion models.
+    Original ported from this codebase:
+    https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42
+    :param betas: a 1-D numpy array of betas for each diffusion timestep,
+                  starting at T and going to 1.
+    """
+
+    def __init__(
+        self,
+        *,
+        betas,
+        model_mean_type,
+        model_var_type,
+        loss_type
+    ):
+
+        self.model_mean_type = model_mean_type
+        self.model_var_type = model_var_type
+        self.loss_type = loss_type
+
+        # Use float64 for accuracy.
+        betas = np.array(betas, dtype=np.float64)
+        self.betas = betas
+        assert len(betas.shape) == 1, "betas must be 1-D"
+        assert (betas > 0).all() and (betas <= 1).all()
+
+        self.num_timesteps = int(betas.shape[0])
+
+        alphas = 1.0 - betas
+        self.alphas_cumprod = np.cumprod(alphas, axis=0)
+        self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1])
+        self.alphas_cumprod_next = np.append(self.alphas_cumprod[1:], 0.0)
+        assert self.alphas_cumprod_prev.shape == (self.num_timesteps,)
+
+        # calculations for diffusion q(x_t | x_{t-1}) and others
+        self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod)
+        self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod)
+        self.log_one_minus_alphas_cumprod = np.log(1.0 - self.alphas_cumprod)
+        self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod)
+        self.sqrt_recipm1_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod - 1)
+
+        # calculations for posterior q(x_{t-1} | x_t, x_0)
+        self.posterior_variance = (
+            betas * (1.0 - self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod)
+        )
+        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain
+        self.posterior_log_variance_clipped = np.log(
+            np.append(self.posterior_variance[1], self.posterior_variance[1:])
+        ) if len(self.posterior_variance) > 1 else np.array([])
+
+        self.posterior_mean_coef1 = (
+            betas * np.sqrt(self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod)
+        )
+        self.posterior_mean_coef2 = (
+            (1.0 - self.alphas_cumprod_prev) * np.sqrt(alphas) / (1.0 - self.alphas_cumprod)
+        )
+
+    def q_mean_variance(self, x_start, t):
+        """
+        Get the distribution q(x_t | x_0).
+        :param x_start: the [N x C x ...] tensor of noiseless inputs.
+        :param t: the number of diffusion steps (minus 1). Here, 0 means one step.
+        :return: A tuple (mean, variance, log_variance), all of x_start's shape.
+        """
+        mean = _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
+        variance = _extract_into_tensor(1.0 - self.alphas_cumprod, t, x_start.shape)
+        log_variance = _extract_into_tensor(self.log_one_minus_alphas_cumprod, t, x_start.shape)
+        return mean, variance, log_variance
+
+    def q_sample(self, x_start, t, noise=None):
+        """
+        Diffuse the data for a given number of diffusion steps.
+        In other words, sample from q(x_t | x_0).
+        :param x_start: the initial data batch.
+        :param t: the number of diffusion steps (minus 1). Here, 0 means one step.
+        :param noise: if specified, the split-out normal noise.
+        :return: A noisy version of x_start.
+        """
+        if noise is None:
+            noise = th.randn_like(x_start)
+        assert noise.shape == x_start.shape
+        return (
+            _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
+            + _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
+        )
+
+    def q_posterior_mean_variance(self, x_start, x_t, t):
+        """
+        Compute the mean and variance of the diffusion posterior:
+            q(x_{t-1} | x_t, x_0)
+        """
+        assert x_start.shape == x_t.shape
+        posterior_mean = (
+            _extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) * x_start
+            + _extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) * x_t
+        )
+        posterior_variance = _extract_into_tensor(self.posterior_variance, t, x_t.shape)
+        posterior_log_variance_clipped = _extract_into_tensor(
+            self.posterior_log_variance_clipped, t, x_t.shape
+        )
+        assert (
+            posterior_mean.shape[0]
+            == posterior_variance.shape[0]
+            == posterior_log_variance_clipped.shape[0]
+            == x_start.shape[0]
+        )
+        return posterior_mean, posterior_variance, posterior_log_variance_clipped
+
+    def p_mean_variance(self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None):
+        """
+        Apply the model to get p(x_{t-1} | x_t), as well as a prediction of
+        the initial x, x_0.
+        :param model: the model, which takes a signal and a batch of timesteps
+                      as input.
+        :param x: the [N x C x ...] tensor at time t.
+        :param t: a 1-D Tensor of timesteps.
+        :param clip_denoised: if True, clip the denoised signal into [-1, 1].
+        :param denoised_fn: if not None, a function which applies to the
+            x_start prediction before it is used to sample. Applies before
+            clip_denoised.
+        :param model_kwargs: if not None, a dict of extra keyword arguments to
+            pass to the model. This can be used for conditioning.
+        :return: a dict with the following keys:
+                 - 'mean': the model mean output.
+                 - 'variance': the model variance output.
+                 - 'log_variance': the log of 'variance'.
+                 - 'pred_xstart': the prediction for x_0.
+        """
+        if model_kwargs is None:
+            model_kwargs = {}
+
+        B, C = x.shape[:2]
+        assert t.shape == (B,)
+        model_output = model(x, t, **model_kwargs)
+        if isinstance(model_output, tuple):
+            model_output, extra = model_output
+        else:
+            extra = None
+
+        if self.model_var_type in [ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE]:
+            assert model_output.shape == (B, C * 2, *x.shape[2:])
+            model_output, model_var_values = th.split(model_output, C, dim=1)
+            min_log = _extract_into_tensor(self.posterior_log_variance_clipped, t, x.shape)
+            max_log = _extract_into_tensor(np.log(self.betas), t, x.shape)
+            # The model_var_values is [-1, 1] for [min_var, max_var].
+            frac = (model_var_values + 1) / 2
+            model_log_variance = frac * max_log + (1 - frac) * min_log
+            model_variance = th.exp(model_log_variance)
+        else:
+            model_variance, model_log_variance = {
+                # for fixedlarge, we set the initial (log-)variance like so
+                # to get a better decoder log likelihood.
+                ModelVarType.FIXED_LARGE: (
+                    np.append(self.posterior_variance[1], self.betas[1:]),
+                    np.log(np.append(self.posterior_variance[1], self.betas[1:])),
+                ),
+                ModelVarType.FIXED_SMALL: (
+                    self.posterior_variance,
+                    self.posterior_log_variance_clipped,
+                ),
+            }[self.model_var_type]
+            model_variance = _extract_into_tensor(model_variance, t, x.shape)
+            model_log_variance = _extract_into_tensor(model_log_variance, t, x.shape)
+
+        def process_xstart(x):
+            if denoised_fn is not None:
+                x = denoised_fn(x)
+            if clip_denoised:
+                return x.clamp(-1, 1)
+            return x
+
+        if self.model_mean_type == ModelMeanType.START_X:
+            pred_xstart = process_xstart(model_output)
+        else:
+            pred_xstart = process_xstart(
+                self._predict_xstart_from_eps(x_t=x, t=t, eps=model_output)
+            )
+        model_mean, _, _ = self.q_posterior_mean_variance(x_start=pred_xstart, x_t=x, t=t)
+
+        assert model_mean.shape == model_log_variance.shape == pred_xstart.shape == x.shape
+        return {
+            "mean": model_mean,
+            "variance": model_variance,
+            "log_variance": model_log_variance,
+            "pred_xstart": pred_xstart,
+            "extra": extra,
+        }
+
+    def _predict_xstart_from_eps(self, x_t, t, eps):
+        assert x_t.shape == eps.shape
+        return (
+            _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t
+            - _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * eps
+        )
+
+    def _predict_eps_from_xstart(self, x_t, t, pred_xstart):
+        return (
+            _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - pred_xstart
+        ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
+
+    def condition_mean(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
+        """
+        Compute the mean for the previous step, given a function cond_fn that
+        computes the gradient of a conditional log probability with respect to
+        x. In particular, cond_fn computes grad(log(p(y|x))), and we want to
+        condition on y.
+        This uses the conditioning strategy from Sohl-Dickstein et al. (2015).
+        """
+        gradient = cond_fn(x, t, **model_kwargs)
+        new_mean = p_mean_var["mean"].float() + p_mean_var["variance"] * gradient.float()
+        return new_mean
+
+    def condition_score(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
+        """
+        Compute what the p_mean_variance output would have been, should the
+        model's score function be conditioned by cond_fn.
+        See condition_mean() for details on cond_fn.
+        Unlike condition_mean(), this instead uses the conditioning strategy
+        from Song et al (2020).
+        """
+        alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
+
+        eps = self._predict_eps_from_xstart(x, t, p_mean_var["pred_xstart"])
+        eps = eps - (1 - alpha_bar).sqrt() * cond_fn(x, t, **model_kwargs)
+
+        out = p_mean_var.copy()
+        out["pred_xstart"] = self._predict_xstart_from_eps(x, t, eps)
+        out["mean"], _, _ = self.q_posterior_mean_variance(x_start=out["pred_xstart"], x_t=x, t=t)
+        return out
+
+    def p_sample(
+        self,
+        model,
+        x,
+        t,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+    ):
+        """
+        Sample x_{t-1} from the model at the given timestep.
+        :param model: the model to sample from.
+        :param x: the current tensor at x_{t-1}.
+        :param t: the value of t, starting at 0 for the first diffusion step.
+        :param clip_denoised: if True, clip the x_start prediction to [-1, 1].
+        :param denoised_fn: if not None, a function which applies to the
+            x_start prediction before it is used to sample.
+        :param cond_fn: if not None, this is a gradient function that acts
+                        similarly to the model.
+        :param model_kwargs: if not None, a dict of extra keyword arguments to
+            pass to the model. This can be used for conditioning.
+        :return: a dict containing the following keys:
+                 - 'sample': a random sample from the model.
+                 - 'pred_xstart': a prediction of x_0.
+        """
+        out = self.p_mean_variance(
+            model,
+            x,
+            t,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            model_kwargs=model_kwargs,
+        )
+        noise = th.randn_like(x)
+        nonzero_mask = (
+            (t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
+        )  # no noise when t == 0
+        if cond_fn is not None:
+            out["mean"] = self.condition_mean(cond_fn, out, x, t, model_kwargs=model_kwargs)
+        sample = out["mean"] + nonzero_mask * th.exp(0.5 * out["log_variance"]) * noise
+        return {"sample": sample, "pred_xstart": out["pred_xstart"]}
+
+    def p_sample_loop(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+    ):
+        """
+        Generate samples from the model.
+        :param model: the model module.
+        :param shape: the shape of the samples, (N, C, H, W).
+        :param noise: if specified, the noise from the encoder to sample.
+                      Should be of the same shape as `shape`.
+        :param clip_denoised: if True, clip x_start predictions to [-1, 1].
+        :param denoised_fn: if not None, a function which applies to the
+            x_start prediction before it is used to sample.
+        :param cond_fn: if not None, this is a gradient function that acts
+                        similarly to the model.
+        :param model_kwargs: if not None, a dict of extra keyword arguments to
+            pass to the model. This can be used for conditioning.
+        :param device: if specified, the device to create the samples on.
+                       If not specified, use a model parameter's device.
+        :param progress: if True, show a tqdm progress bar.
+        :return: a non-differentiable batch of samples.
+        """
+        final = None
+        for sample in self.p_sample_loop_progressive(
+            model,
+            shape,
+            noise=noise,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            cond_fn=cond_fn,
+            model_kwargs=model_kwargs,
+            device=device,
+            progress=progress,
+        ):
+            final = sample
+        return final["sample"]
+
+    def p_sample_loop_progressive(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+    ):
+        """
+        Generate samples from the model and yield intermediate samples from
+        each timestep of diffusion.
+        Arguments are the same as p_sample_loop().
+        Returns a generator over dicts, where each dict is the return value of
+        p_sample().
+        """
+        if device is None:
+            device = next(model.parameters()).device
+        assert isinstance(shape, (tuple, list))
+        if noise is not None:
+            img = noise
+        else:
+            img = th.randn(*shape, device=device)
+        indices = list(range(self.num_timesteps))[::-1]
+
+        if progress:
+            # Lazy import so that we don't depend on tqdm.
+            from tqdm.auto import tqdm
+
+            indices = tqdm(indices)
+
+        for i in indices:
+            t = th.tensor([i] * shape[0], device=device)
+            with th.no_grad():
+                out = self.p_sample(
+                    model,
+                    img,
+                    t,
+                    clip_denoised=clip_denoised,
+                    denoised_fn=denoised_fn,
+                    cond_fn=cond_fn,
+                    model_kwargs=model_kwargs,
+                )
+                yield out
+                img = out["sample"]
+
+    def ddim_sample(
+        self,
+        model,
+        x,
+        t,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        eta=0.0,
+    ):
+        """
+        Sample x_{t-1} from the model using DDIM.
+        Same usage as p_sample().
+        """
+        out = self.p_mean_variance(
+            model,
+            x,
+            t,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            model_kwargs=model_kwargs,
+        )
+        if cond_fn is not None:
+            out = self.condition_score(cond_fn, out, x, t, model_kwargs=model_kwargs)
+
+        # Usually our model outputs epsilon, but we re-derive it
+        # in case we used x_start or x_prev prediction.
+        eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
+
+        alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
+        alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t, x.shape)
+        sigma = (
+            eta
+            * th.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar))
+            * th.sqrt(1 - alpha_bar / alpha_bar_prev)
+        )
+        # Equation 12.
+        noise = th.randn_like(x)
+        mean_pred = (
+            out["pred_xstart"] * th.sqrt(alpha_bar_prev)
+            + th.sqrt(1 - alpha_bar_prev - sigma ** 2) * eps
+        )
+        nonzero_mask = (
+            (t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
+        )  # no noise when t == 0
+        sample = mean_pred + nonzero_mask * sigma * noise
+        return {"sample": sample, "pred_xstart": out["pred_xstart"]}
+
+    def ddim_reverse_sample(
+        self,
+        model,
+        x,
+        t,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        eta=0.0,
+    ):
+        """
+        Sample x_{t+1} from the model using DDIM reverse ODE.
+        """
+        assert eta == 0.0, "Reverse ODE only for deterministic path"
+        out = self.p_mean_variance(
+            model,
+            x,
+            t,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            model_kwargs=model_kwargs,
+        )
+        if cond_fn is not None:
+            out = self.condition_score(cond_fn, out, x, t, model_kwargs=model_kwargs)
+        # Usually our model outputs epsilon, but we re-derive it
+        # in case we used x_start or x_prev prediction.
+        eps = (
+            _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x.shape) * x
+            - out["pred_xstart"]
+        ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x.shape)
+        alpha_bar_next = _extract_into_tensor(self.alphas_cumprod_next, t, x.shape)
+
+        # Equation 12. reversed
+        mean_pred = out["pred_xstart"] * th.sqrt(alpha_bar_next) + th.sqrt(1 - alpha_bar_next) * eps
+
+        return {"sample": mean_pred, "pred_xstart": out["pred_xstart"]}
+
+    def ddim_sample_loop(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+        eta=0.0,
+    ):
+        """
+        Generate samples from the model using DDIM.
+        Same usage as p_sample_loop().
+        """
+        final = None
+        for sample in self.ddim_sample_loop_progressive(
+            model,
+            shape,
+            noise=noise,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            cond_fn=cond_fn,
+            model_kwargs=model_kwargs,
+            device=device,
+            progress=progress,
+            eta=eta,
+        ):
+            final = sample
+        return final["sample"]
+
+    def ddim_sample_loop_progressive(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+        eta=0.0,
+    ):
+        """
+        Use DDIM to sample from the model and yield intermediate samples from
+        each timestep of DDIM.
+        Same usage as p_sample_loop_progressive().
+        """
+        if device is None:
+            device = next(model.parameters()).device
+        assert isinstance(shape, (tuple, list))
+        if noise is not None:
+            img = noise
+        else:
+            img = th.randn(*shape, device=device)
+        indices = list(range(self.num_timesteps))[::-1]
+
+        if progress:
+            # Lazy import so that we don't depend on tqdm.
+            from tqdm.auto import tqdm
+
+            indices = tqdm(indices)
+
+        for i in indices:
+            t = th.tensor([i] * shape[0], device=device)
+            with th.no_grad():
+                out = self.ddim_sample(
+                    model,
+                    img,
+                    t,
+                    clip_denoised=clip_denoised,
+                    denoised_fn=denoised_fn,
+                    cond_fn=cond_fn,
+                    model_kwargs=model_kwargs,
+                    eta=eta,
+                )
+                yield out
+                img = out["sample"]
+
+    def _vb_terms_bpd(
+            self, model, x_start, x_t, t, clip_denoised=True, model_kwargs=None
+    ):
+        """
+        Get a term for the variational lower-bound.
+        The resulting units are bits (rather than nats, as one might expect).
+        This allows for comparison to other papers.
+        :return: a dict with the following keys:
+                 - 'output': a shape [N] tensor of NLLs or KLs.
+                 - 'pred_xstart': the x_0 predictions.
+        """
+        true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance(
+            x_start=x_start, x_t=x_t, t=t
+        )
+        out = self.p_mean_variance(
+            model, x_t, t, clip_denoised=clip_denoised, model_kwargs=model_kwargs
+        )
+        kl = normal_kl(
+            true_mean, true_log_variance_clipped, out["mean"], out["log_variance"]
+        )
+        kl = mean_flat(kl) / np.log(2.0)
+
+        decoder_nll = -discretized_gaussian_log_likelihood(
+            x_start, means=out["mean"], log_scales=0.5 * out["log_variance"]
+        )
+        assert decoder_nll.shape == x_start.shape
+        decoder_nll = mean_flat(decoder_nll) / np.log(2.0)
+
+        # At the first timestep return the decoder NLL,
+        # otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t))
+        output = th.where((t == 0), decoder_nll, kl)
+        return {"output": output, "pred_xstart": out["pred_xstart"]}
+
+    def training_losses(self, model, x_start, t, model_kwargs=None, noise=None):
+        """
+        Compute training losses for a single timestep.
+        :param model: the model to evaluate loss on.
+        :param x_start: the [N x C x ...] tensor of inputs.
+        :param t: a batch of timestep indices.
+        :param model_kwargs: if not None, a dict of extra keyword arguments to
+            pass to the model. This can be used for conditioning.
+        :param noise: if specified, the specific Gaussian noise to try to remove.
+        :return: a dict with the key "loss" containing a tensor of shape [N].
+                 Some mean or variance settings may also have other keys.
+        """
+        if model_kwargs is None:
+            model_kwargs = {}
+        if noise is None:
+            noise = th.randn_like(x_start)
+        x_t = self.q_sample(x_start, t, noise=noise)
+
+        terms = {}
+
+        if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL:
+            terms["loss"] = self._vb_terms_bpd(
+                model=model,
+                x_start=x_start,
+                x_t=x_t,
+                t=t,
+                clip_denoised=False,
+                model_kwargs=model_kwargs,
+            )["output"]
+            if self.loss_type == LossType.RESCALED_KL:
+                terms["loss"] *= self.num_timesteps
+        elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE:
+            model_output = model(x_t, t, **model_kwargs)
+
+            if self.model_var_type in [
+                ModelVarType.LEARNED,
+                ModelVarType.LEARNED_RANGE,
+            ]:
+                B, C = x_t.shape[:2]
+                assert model_output.shape == (B, C * 2, *x_t.shape[2:])
+                model_output, model_var_values = th.split(model_output, C, dim=1)
+                # Learn the variance using the variational bound, but don't let
+                # it affect our mean prediction.
+                frozen_out = th.cat([model_output.detach(), model_var_values], dim=1)
+                terms["vb"] = self._vb_terms_bpd(
+                    model=lambda *args, r=frozen_out: r,
+                    x_start=x_start,
+                    x_t=x_t,
+                    t=t,
+                    clip_denoised=False,
+                )["output"]
+                if self.loss_type == LossType.RESCALED_MSE:
+                    # Divide by 1000 for equivalence with initial implementation.
+                    # Without a factor of 1/1000, the VB term hurts the MSE term.
+                    terms["vb"] *= self.num_timesteps / 1000.0
+
+            target = {
+                ModelMeanType.PREVIOUS_X: self.q_posterior_mean_variance(
+                    x_start=x_start, x_t=x_t, t=t
+                )[0],
+                ModelMeanType.START_X: x_start,
+                ModelMeanType.EPSILON: noise,
+            }[self.model_mean_type]
+            assert model_output.shape == target.shape == x_start.shape
+            terms["mse"] = mean_flat((target - model_output) ** 2)
+            if "vb" in terms:
+                terms["loss"] = terms["mse"] + terms["vb"]
+            else:
+                terms["loss"] = terms["mse"]
+        else:
+            raise NotImplementedError(self.loss_type)
+
+        return terms
+
+    def _prior_bpd(self, x_start):
+        """
+        Get the prior KL term for the variational lower-bound, measured in
+        bits-per-dim.
+        This term can't be optimized, as it only depends on the encoder.
+        :param x_start: the [N x C x ...] tensor of inputs.
+        :return: a batch of [N] KL values (in bits), one per batch element.
+        """
+        batch_size = x_start.shape[0]
+        t = th.tensor([self.num_timesteps - 1] * batch_size, device=x_start.device)
+        qt_mean, _, qt_log_variance = self.q_mean_variance(x_start, t)
+        kl_prior = normal_kl(
+            mean1=qt_mean, logvar1=qt_log_variance, mean2=0.0, logvar2=0.0
+        )
+        return mean_flat(kl_prior) / np.log(2.0)
+
+    def calc_bpd_loop(self, model, x_start, clip_denoised=True, model_kwargs=None):
+        """
+        Compute the entire variational lower-bound, measured in bits-per-dim,
+        as well as other related quantities.
+        :param model: the model to evaluate loss on.
+        :param x_start: the [N x C x ...] tensor of inputs.
+        :param clip_denoised: if True, clip denoised samples.
+        :param model_kwargs: if not None, a dict of extra keyword arguments to
+            pass to the model. This can be used for conditioning.
+        :return: a dict containing the following keys:
+                 - total_bpd: the total variational lower-bound, per batch element.
+                 - prior_bpd: the prior term in the lower-bound.
+                 - vb: an [N x T] tensor of terms in the lower-bound.
+                 - xstart_mse: an [N x T] tensor of x_0 MSEs for each timestep.
+                 - mse: an [N x T] tensor of epsilon MSEs for each timestep.
+        """
+        device = x_start.device
+        batch_size = x_start.shape[0]
+
+        vb = []
+        xstart_mse = []
+        mse = []
+        for t in list(range(self.num_timesteps))[::-1]:
+            t_batch = th.tensor([t] * batch_size, device=device)
+            noise = th.randn_like(x_start)
+            x_t = self.q_sample(x_start=x_start, t=t_batch, noise=noise)
+            # Calculate VLB term at the current timestep
+            with th.no_grad():
+                out = self._vb_terms_bpd(
+                    model,
+                    x_start=x_start,
+                    x_t=x_t,
+                    t=t_batch,
+                    clip_denoised=clip_denoised,
+                    model_kwargs=model_kwargs,
+                )
+            vb.append(out["output"])
+            xstart_mse.append(mean_flat((out["pred_xstart"] - x_start) ** 2))
+            eps = self._predict_eps_from_xstart(x_t, t_batch, out["pred_xstart"])
+            mse.append(mean_flat((eps - noise) ** 2))
+
+        vb = th.stack(vb, dim=1)
+        xstart_mse = th.stack(xstart_mse, dim=1)
+        mse = th.stack(mse, dim=1)
+
+        prior_bpd = self._prior_bpd(x_start)
+        total_bpd = vb.sum(dim=1) + prior_bpd
+        return {
+            "total_bpd": total_bpd,
+            "prior_bpd": prior_bpd,
+            "vb": vb,
+            "xstart_mse": xstart_mse,
+            "mse": mse,
+        }
+
+
+def _extract_into_tensor(arr, timesteps, broadcast_shape):
+    """
+    Extract values from a 1-D numpy array for a batch of indices.
+    :param arr: the 1-D numpy array.
+    :param timesteps: a tensor of indices into the array to extract.
+    :param broadcast_shape: a larger shape of K dimensions with the batch
+                            dimension equal to the length of timesteps.
+    :return: a tensor of shape [batch_size, 1, ...] where the shape has K dims.
+    """
+    res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float()
+    while len(res.shape) < len(broadcast_shape):
+        res = res[..., None]
+    return res + th.zeros(broadcast_shape, device=timesteps.device)

diffusion/respace.py

@@ -0,0 +1,129 @@
+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+import numpy as np
+import torch as th
+
+from .gaussian_diffusion import GaussianDiffusion
+
+
+def space_timesteps(num_timesteps, section_counts):
+    """
+    Create a list of timesteps to use from an original diffusion process,
+    given the number of timesteps we want to take from equally-sized portions
+    of the original process.
+    For example, if there's 300 timesteps and the section counts are [10,15,20]
+    then the first 100 timesteps are strided to be 10 timesteps, the second 100
+    are strided to be 15 timesteps, and the final 100 are strided to be 20.
+    If the stride is a string starting with "ddim", then the fixed striding
+    from the DDIM paper is used, and only one section is allowed.
+    :param num_timesteps: the number of diffusion steps in the original
+                          process to divide up.
+    :param section_counts: either a list of numbers, or a string containing
+                           comma-separated numbers, indicating the step count
+                           per section. As a special case, use "ddimN" where N
+                           is a number of steps to use the striding from the
+                           DDIM paper.
+    :return: a set of diffusion steps from the original process to use.
+    """
+    if isinstance(section_counts, str):
+        if section_counts.startswith("ddim"):
+            desired_count = int(section_counts[len("ddim") :])
+            for i in range(1, num_timesteps):
+                if len(range(0, num_timesteps, i)) == desired_count:
+                    return set(range(0, num_timesteps, i))
+            raise ValueError(
+                f"cannot create exactly {num_timesteps} steps with an integer stride"
+            )
+        section_counts = [int(x) for x in section_counts.split(",")]
+    size_per = num_timesteps // len(section_counts)
+    extra = num_timesteps % len(section_counts)
+    start_idx = 0
+    all_steps = []
+    for i, section_count in enumerate(section_counts):
+        size = size_per + (1 if i < extra else 0)
+        if size < section_count:
+            raise ValueError(
+                f"cannot divide section of {size} steps into {section_count}"
+            )
+        if section_count <= 1:
+            frac_stride = 1
+        else:
+            frac_stride = (size - 1) / (section_count - 1)
+        cur_idx = 0.0
+        taken_steps = []
+        for _ in range(section_count):
+            taken_steps.append(start_idx + round(cur_idx))
+            cur_idx += frac_stride
+        all_steps += taken_steps
+        start_idx += size
+    return set(all_steps)
+
+
+class SpacedDiffusion(GaussianDiffusion):
+    """
+    A diffusion process which can skip steps in a base diffusion process.
+    :param use_timesteps: a collection (sequence or set) of timesteps from the
+                          original diffusion process to retain.
+    :param kwargs: the kwargs to create the base diffusion process.
+    """
+
+    def __init__(self, use_timesteps, **kwargs):
+        self.use_timesteps = set(use_timesteps)
+        self.timestep_map = []
+        self.original_num_steps = len(kwargs["betas"])
+
+        base_diffusion = GaussianDiffusion(**kwargs)  # pylint: disable=missing-kwoa
+        last_alpha_cumprod = 1.0
+        new_betas = []
+        for i, alpha_cumprod in enumerate(base_diffusion.alphas_cumprod):
+            if i in self.use_timesteps:
+                new_betas.append(1 - alpha_cumprod / last_alpha_cumprod)
+                last_alpha_cumprod = alpha_cumprod
+                self.timestep_map.append(i)
+        kwargs["betas"] = np.array(new_betas)
+        super().__init__(**kwargs)
+
+    def p_mean_variance(
+        self, model, *args, **kwargs
+    ):  # pylint: disable=signature-differs
+        return super().p_mean_variance(self._wrap_model(model), *args, **kwargs)
+
+    def training_losses(
+        self, model, *args, **kwargs
+    ):  # pylint: disable=signature-differs
+        return super().training_losses(self._wrap_model(model), *args, **kwargs)
+
+    def condition_mean(self, cond_fn, *args, **kwargs):
+        return super().condition_mean(self._wrap_model(cond_fn), *args, **kwargs)
+
+    def condition_score(self, cond_fn, *args, **kwargs):
+        return super().condition_score(self._wrap_model(cond_fn), *args, **kwargs)
+
+    def _wrap_model(self, model):
+        if isinstance(model, _WrappedModel):
+            return model
+        return _WrappedModel(
+            model, self.timestep_map, self.original_num_steps
+        )
+
+    def _scale_timesteps(self, t):
+        # Scaling is done by the wrapped model.
+        return t
+
+
+class _WrappedModel:
+    def __init__(self, model, timestep_map, original_num_steps):
+        self.model = model
+        self.timestep_map = timestep_map
+        # self.rescale_timesteps = rescale_timesteps
+        self.original_num_steps = original_num_steps
+
+    def __call__(self, x, ts, **kwargs):
+        map_tensor = th.tensor(self.timestep_map, device=ts.device, dtype=ts.dtype)
+        new_ts = map_tensor[ts]
+        # if self.rescale_timesteps:
+        #     new_ts = new_ts.float() * (1000.0 / self.original_num_steps)
+        return self.model(x, new_ts, **kwargs)

diffusion/timestep_sampler.py

@@ -0,0 +1,150 @@
+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+from abc import ABC, abstractmethod
+
+import numpy as np
+import torch as th
+import torch.distributed as dist
+
+
+def create_named_schedule_sampler(name, diffusion):
+    """
+    Create a ScheduleSampler from a library of pre-defined samplers.
+    :param name: the name of the sampler.
+    :param diffusion: the diffusion object to sample for.
+    """
+    if name == "uniform":
+        return UniformSampler(diffusion)
+    elif name == "loss-second-moment":
+        return LossSecondMomentResampler(diffusion)
+    else:
+        raise NotImplementedError(f"unknown schedule sampler: {name}")
+
+
+class ScheduleSampler(ABC):
+    """
+    A distribution over timesteps in the diffusion process, intended to reduce
+    variance of the objective.
+    By default, samplers perform unbiased importance sampling, in which the
+    objective's mean is unchanged.
+    However, subclasses may override sample() to change how the resampled
+    terms are reweighted, allowing for actual changes in the objective.
+    """
+
+    @abstractmethod
+    def weights(self):
+        """
+        Get a numpy array of weights, one per diffusion step.
+        The weights needn't be normalized, but must be positive.
+        """
+
+    def sample(self, batch_size, device):
+        """
+        Importance-sample timesteps for a batch.
+        :param batch_size: the number of timesteps.
+        :param device: the torch device to save to.
+        :return: a tuple (timesteps, weights):
+                 - timesteps: a tensor of timestep indices.
+                 - weights: a tensor of weights to scale the resulting losses.
+        """
+        w = self.weights()
+        p = w / np.sum(w)
+        indices_np = np.random.choice(len(p), size=(batch_size,), p=p)
+        indices = th.from_numpy(indices_np).long().to(device)
+        weights_np = 1 / (len(p) * p[indices_np])
+        weights = th.from_numpy(weights_np).float().to(device)
+        return indices, weights
+
+
+class UniformSampler(ScheduleSampler):
+    def __init__(self, diffusion):
+        self.diffusion = diffusion
+        self._weights = np.ones([diffusion.num_timesteps])
+
+    def weights(self):
+        return self._weights
+
+
+class LossAwareSampler(ScheduleSampler):
+    def update_with_local_losses(self, local_ts, local_losses):
+        """
+        Update the reweighting using losses from a model.
+        Call this method from each rank with a batch of timesteps and the
+        corresponding losses for each of those timesteps.
+        This method will perform synchronization to make sure all of the ranks
+        maintain the exact same reweighting.
+        :param local_ts: an integer Tensor of timesteps.
+        :param local_losses: a 1D Tensor of losses.
+        """
+        batch_sizes = [
+            th.tensor([0], dtype=th.int32, device=local_ts.device)
+            for _ in range(dist.get_world_size())
+        ]
+        dist.all_gather(
+            batch_sizes,
+            th.tensor([len(local_ts)], dtype=th.int32, device=local_ts.device),
+        )
+
+        # Pad all_gather batches to be the maximum batch size.
+        batch_sizes = [x.item() for x in batch_sizes]
+        max_bs = max(batch_sizes)
+
+        timestep_batches = [th.zeros(max_bs).to(local_ts) for bs in batch_sizes]
+        loss_batches = [th.zeros(max_bs).to(local_losses) for bs in batch_sizes]
+        dist.all_gather(timestep_batches, local_ts)
+        dist.all_gather(loss_batches, local_losses)
+        timesteps = [
+            x.item() for y, bs in zip(timestep_batches, batch_sizes) for x in y[:bs]
+        ]
+        losses = [x.item() for y, bs in zip(loss_batches, batch_sizes) for x in y[:bs]]
+        self.update_with_all_losses(timesteps, losses)
+
+    @abstractmethod
+    def update_with_all_losses(self, ts, losses):
+        """
+        Update the reweighting using losses from a model.
+        Sub-classes should override this method to update the reweighting
+        using losses from the model.
+        This method directly updates the reweighting without synchronizing
+        between workers. It is called by update_with_local_losses from all
+        ranks with identical arguments. Thus, it should have deterministic
+        behavior to maintain state across workers.
+        :param ts: a list of int timesteps.
+        :param losses: a list of float losses, one per timestep.
+        """
+
+
+class LossSecondMomentResampler(LossAwareSampler):
+    def __init__(self, diffusion, history_per_term=10, uniform_prob=0.001):
+        self.diffusion = diffusion
+        self.history_per_term = history_per_term
+        self.uniform_prob = uniform_prob
+        self._loss_history = np.zeros(
+            [diffusion.num_timesteps, history_per_term], dtype=np.float64
+        )
+        self._loss_counts = np.zeros([diffusion.num_timesteps], dtype=np.int)
+
+    def weights(self):
+        if not self._warmed_up():
+            return np.ones([self.diffusion.num_timesteps], dtype=np.float64)
+        weights = np.sqrt(np.mean(self._loss_history ** 2, axis=-1))
+        weights /= np.sum(weights)
+        weights *= 1 - self.uniform_prob
+        weights += self.uniform_prob / len(weights)
+        return weights
+
+    def update_with_all_losses(self, ts, losses):
+        for t, loss in zip(ts, losses):
+            if self._loss_counts[t] == self.history_per_term:
+                # Shift out the oldest loss term.
+                self._loss_history[t, :-1] = self._loss_history[t, 1:]
+                self._loss_history[t, -1] = loss
+            else:
+                self._loss_history[t, self._loss_counts[t]] = loss
+                self._loss_counts[t] += 1
+
+    def _warmed_up(self):
+        return (self._loss_counts == self.history_per_term).all()

models.py

@@ -0,0 +1,576 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+# --------------------------------------------------------
+# References:
+# GLIDE: https://github.com/openai/glide-text2im
+# MAE: https://github.com/facebookresearch/mae/blob/main/models_mae.py
+# --------------------------------------------------------
+
+import torch
+import torch.nn as nn
+import numpy as np
+import math
+from timm.models.vision_transformer import PatchEmbed, Attention, Mlp
+
+import torch.nn.functional as F
+
+
+def modulate(x, shift, scale):
+    return x * (1 + scale.unsqueeze(1)) + shift.unsqueeze(1)
+
+
+#################################################################################
+#               Embedding Layers for Timesteps and Class Labels                 #
+#################################################################################
+
+class TimestepEmbedder(nn.Module):
+    """
+    Embeds scalar timesteps into vector representations.
+    """
+    def __init__(self, hidden_size, frequency_embedding_size=256):
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(frequency_embedding_size, hidden_size, bias=True),
+            nn.SiLU(),
+            nn.Linear(hidden_size, hidden_size, bias=True),
+        )
+        self.frequency_embedding_size = frequency_embedding_size
+
+    @staticmethod
+    def timestep_embedding(t, dim, max_period=10000):
+        """
+        Create sinusoidal timestep embeddings.
+        :param t: a 1-D Tensor of N indices, one per batch element.
+                          These may be fractional.
+        :param dim: the dimension of the output.
+        :param max_period: controls the minimum frequency of the embeddings.
+        :return: an (N, D) Tensor of positional embeddings.
+        """
+        # https://github.com/openai/glide-text2im/blob/main/glide_text2im/nn.py
+        half = dim // 2
+        freqs = torch.exp(
+            -math.log(max_period) * torch.arange(start=0, end=half, dtype=torch.float32) / half
+        ).to(device=t.device)
+        args = t[:, None].float() * freqs[None]
+        embedding = torch.cat([torch.cos(args), torch.sin(args)], dim=-1)
+        if dim % 2:
+            embedding = torch.cat([embedding, torch.zeros_like(embedding[:, :1])], dim=-1)
+        return embedding
+
+    def forward(self, t):
+        t_freq = self.timestep_embedding(t, self.frequency_embedding_size)
+        t_emb = self.mlp(t_freq)
+        return t_emb
+
+
+class LabelEmbedder(nn.Module):
+    """
+    Embeds class labels into vector representations. Also handles label dropout for classifier-free guidance.
+    """
+    def __init__(self, num_classes, hidden_size, dropout_prob):
+        super().__init__()
+        use_cfg_embedding = dropout_prob > 0
+        self.embedding_table = nn.Embedding(num_classes + use_cfg_embedding, hidden_size)
+        self.num_classes = num_classes
+        self.dropout_prob = dropout_prob
+
+    def token_drop(self, labels, force_drop_ids=None):
+        """
+        Drops labels to enable classifier-free guidance.
+        """
+        if force_drop_ids is None:
+            drop_ids = torch.rand(labels.shape[0], device=labels.device) < self.dropout_prob
+        else:
+            drop_ids = force_drop_ids == 1
+        labels = torch.where(drop_ids, self.num_classes, labels)
+        return labels
+
+    def forward(self, labels, train, force_drop_ids=None):
+        use_dropout = self.dropout_prob > 0
+        if (train and use_dropout) or (force_drop_ids is not None):
+            labels = self.token_drop(labels, force_drop_ids)
+        embeddings = self.embedding_table(labels)
+        return embeddings
+
+
+#################################################################################
+#                                MoE Layer.                                     #
+#################################################################################
+
+
+
+
+class MoEGate(nn.Module):
+    def __init__(self, embed_dim, num_experts=16, num_experts_per_tok=2, aux_loss_alpha=0.01):
+        super().__init__()
+        self.top_k = num_experts_per_tok
+        self.n_routed_experts = num_experts
+
+        self.scoring_func = 'softmax'
+        self.alpha = aux_loss_alpha
+        self.seq_aux = False
+
+        # topk selection algorithm
+        self.norm_topk_prob = False
+        self.gating_dim = embed_dim
+        self.weight = nn.Parameter(torch.empty((self.n_routed_experts, self.gating_dim)))
+        self.reset_parameters()
+
+    def reset_parameters(self) -> None:
+        import torch.nn.init  as init
+        init.kaiming_uniform_(self.weight, a=math.sqrt(5))
+    
+    def forward(self, hidden_states):
+        bsz, seq_len, h = hidden_states.shape        
+        ### compute gating score
+        hidden_states = hidden_states.view(-1, h)
+        logits = F.linear(hidden_states, self.weight, None)
+        if self.scoring_func == 'softmax':
+            scores = logits.softmax(dim=-1)
+        else:
+            raise NotImplementedError(f'insupportable scoring function for MoE gating: {self.scoring_func}')
+        
+        ### select top-k experts
+        topk_weight, topk_idx = torch.topk(scores, k=self.top_k, dim=-1, sorted=False)
+        
+        ### norm gate to sum 1
+        if self.top_k > 1 and self.norm_topk_prob:
+            denominator = topk_weight.sum(dim=-1, keepdim=True) + 1e-20
+            topk_weight = topk_weight / denominator
+
+        ### expert-level computation auxiliary loss
+        if self.training and self.alpha > 0.0:
+            scores_for_aux = scores
+            aux_topk = self.top_k
+            # always compute aux loss based on the naive greedy topk method
+            topk_idx_for_aux_loss = topk_idx.view(bsz, -1)
+            if self.seq_aux:
+                scores_for_seq_aux = scores_for_aux.view(bsz, seq_len, -1)
+                ce = torch.zeros(bsz, self.n_routed_experts, device=hidden_states.device)
+                ce.scatter_add_(1, topk_idx_for_aux_loss, torch.ones(bsz, seq_len * aux_topk, device=hidden_states.device)).div_(seq_len * aux_topk / self.n_routed_experts)
+                aux_loss = (ce * scores_for_seq_aux.mean(dim = 1)).sum(dim = 1).mean() * self.alpha
+            else:
+                mask_ce = F.one_hot(topk_idx_for_aux_loss.view(-1), num_classes=self.n_routed_experts)
+                ce = mask_ce.float().mean(0)
+                Pi = scores_for_aux.mean(0)
+                fi = ce * self.n_routed_experts
+                aux_loss = (Pi * fi).sum() * self.alpha
+        else:
+            aux_loss = None
+        return topk_idx, topk_weight, aux_loss
+
+
+
+
+class AddAuxiliaryLoss(torch.autograd.Function):
+    """
+    The trick function of adding auxiliary (aux) loss, 
+    which includes the gradient of the aux loss during backpropagation.
+    """
+    @staticmethod
+    def forward(ctx, x, loss):
+        assert loss.numel() == 1
+        ctx.dtype = loss.dtype
+        ctx.required_aux_loss = loss.requires_grad
+        return x
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        grad_loss = None
+        if ctx.required_aux_loss:
+            grad_loss = torch.ones(1, dtype=ctx.dtype, device=grad_output.device)
+        return grad_output, grad_loss
+
+
+
+class MoeMLP(nn.Module):
+    def __init__(self, hidden_size, intermediate_size):
+        super().__init__()
+
+        self.hidden_size = hidden_size
+        self.intermediate_size = intermediate_size
+        self.gate_proj = nn.Linear(self.hidden_size, self.intermediate_size, bias=False)
+        self.up_proj = nn.Linear(self.hidden_size, self.intermediate_size, bias=False)
+        self.down_proj = nn.Linear(self.intermediate_size, self.hidden_size, bias=False)
+        self.act_fn = nn.SiLU()
+        self.pretraining_tp = 2
+
+    def forward(self, x):
+        if self.pretraining_tp > 1:
+            slice = self.intermediate_size // self.pretraining_tp
+            gate_proj_slices = self.gate_proj.weight.split(slice, dim=0)
+            up_proj_slices = self.up_proj.weight.split(slice, dim=0)
+            down_proj_slices = self.down_proj.weight.split(slice, dim=1)
+
+            gate_proj = torch.cat(
+                [F.linear(x, gate_proj_slices[i]) for i in range(self.pretraining_tp)], dim=-1
+            )
+            up_proj = torch.cat([F.linear(x, up_proj_slices[i]) for i in range(self.pretraining_tp)], dim=-1)
+
+            intermediate_states = (self.act_fn(gate_proj) * up_proj).split(slice, dim=-1)
+            down_proj = [
+                F.linear(intermediate_states[i], down_proj_slices[i]) for i in range(self.pretraining_tp)
+            ]
+            down_proj = sum(down_proj)
+        else:
+            down_proj = self.down_proj(self.act_fn(self.gate_proj(x)) * self.up_proj(x))
+
+        return down_proj
+
+
+class SparseMoeBlock(nn.Module):
+    """
+    A mixed expert module containing shared experts.
+    """
+    def __init__(self, embed_dim, mlp_ratio=4, num_experts=16, num_experts_per_tok=2):
+        super().__init__()
+        self.num_experts_per_tok = num_experts_per_tok
+        self.experts = nn.ModuleList([MoeMLP(hidden_size = embed_dim, intermediate_size = mlp_ratio * embed_dim) for i in range(num_experts)])
+        self.gate = MoEGate(embed_dim=embed_dim, num_experts=num_experts, num_experts_per_tok=num_experts_per_tok)
+        self.n_shared_experts = 2
+        
+        if self.n_shared_experts is not None:
+            intermediate_size =  embed_dim * self.n_shared_experts
+            self.shared_experts = MoeMLP(hidden_size = embed_dim, intermediate_size = intermediate_size)
+    
+    def forward(self, hidden_states):
+        identity = hidden_states
+        orig_shape = hidden_states.shape
+        topk_idx, topk_weight, aux_loss = self.gate(hidden_states)
+        hidden_states = hidden_states.view(-1, hidden_states.shape[-1])
+        flat_topk_idx = topk_idx.view(-1)
+        if self.training:
+            hidden_states = hidden_states.repeat_interleave(self.num_experts_per_tok, dim=0)
+            y = torch.empty_like(hidden_states)
+            for i, expert in enumerate(self.experts):
+                y[flat_topk_idx == i] = expert(hidden_states[flat_topk_idx == i])
+            y = (y.view(*topk_weight.shape, -1) * topk_weight.unsqueeze(-1)).sum(dim=1)
+            y =  y.view(*orig_shape)
+            y = AddAuxiliaryLoss.apply(y, aux_loss)
+        else:
+            y = self.moe_infer(hidden_states, flat_topk_idx, topk_weight.view(-1, 1)).view(*orig_shape)
+        if self.n_shared_experts is not None:
+            y = y + self.shared_experts(identity)
+        return y
+    
+
+    @torch.no_grad()
+    def moe_infer(self, x, flat_expert_indices, flat_expert_weights):
+        expert_cache = torch.zeros_like(x)
+        idxs = flat_expert_indices.argsort()
+        tokens_per_expert = flat_expert_indices.bincount().cpu().numpy().cumsum(0)
+        token_idxs = idxs // self.num_experts_per_tok
+        for i, end_idx in enumerate(tokens_per_expert):
+            start_idx = 0 if i == 0 else tokens_per_expert[i-1]
+            if start_idx == end_idx:
+                continue
+            expert = self.experts[i]
+            exp_token_idx = token_idxs[start_idx:end_idx]
+            expert_tokens = x[exp_token_idx]
+            expert_out = expert(expert_tokens)
+            expert_out.mul_(flat_expert_weights[idxs[start_idx:end_idx]])
+            expert_cache.scatter_reduce_(0, exp_token_idx.view(-1, 1).repeat(1, x.shape[-1]), expert_out, reduce='sum')
+        return expert_cache
+
+
+class RMSNorm(nn.Module):
+    def __init__(self, hidden_size, eps=1e-6):
+        """
+        MambaRMSNorm is equivalent to T5LayerNorm
+        """
+        super().__init__()
+        self.weight = nn.Parameter(torch.ones(hidden_size))
+        self.variance_epsilon = eps
+
+    def forward(self, hidden_states):
+        input_dtype = hidden_states.dtype
+        hidden_states = hidden_states.to(torch.float32)
+        variance = hidden_states.pow(2).mean(-1, keepdim=True)
+        hidden_states = hidden_states * torch.rsqrt(variance + self.variance_epsilon)
+        return self.weight * hidden_states.to(input_dtype)
+
+
+
+
+#################################################################################
+#                                 Core DiT Model                                #
+#################################################################################
+
+class DiTBlock(nn.Module):
+    """
+    A DiT block with adaptive layer norm zero (adaLN-Zero) conditioning.
+    """
+    def __init__(
+        self, hidden_size, num_heads, mlp_ratio=4,
+        num_experts=8, num_experts_per_tok=2, **block_kwargs
+    ):
+        super().__init__()
+        self.norm1 = nn.LayerNorm(hidden_size, elementwise_affine=False, eps=1e-6)
+        self.attn = Attention(hidden_size, num_heads=num_heads, qkv_bias=True, **block_kwargs)
+        self.norm2 = nn.LayerNorm(hidden_size, elementwise_affine=False, eps=1e-6)
+        mlp_hidden_dim = int(hidden_size * mlp_ratio)
+        approx_gelu = lambda: nn.GELU(approximate="tanh")
+        # self.mlp = Mlp(in_features=hidden_size, hidden_features=mlp_hidden_dim, act_layer=approx_gelu, drop=0) 
+        self.moe = SparseMoeBlock(hidden_size, mlp_ratio, num_experts, num_experts_per_tok)
+
+        self.adaLN_modulation = nn.Sequential(
+            nn.SiLU(),
+            nn.Linear(hidden_size, 6 * hidden_size, bias=True)
+        )
+
+    def forward(self, x, c):
+        shift_msa, scale_msa, gate_msa, shift_mlp, scale_mlp, gate_mlp = self.adaLN_modulation(c).chunk(6, dim=1)
+        x = x + gate_msa.unsqueeze(1) * self.attn(modulate(self.norm1(x), shift_msa, scale_msa)) 
+        x = x + gate_mlp.unsqueeze(1) * self.moe(modulate(self.norm2(x), shift_mlp, scale_mlp))
+        return x
+
+
+class FinalLayer(nn.Module):
+    """
+    The final layer of DiT.
+    """
+    def __init__(self, hidden_size, patch_size, out_channels):
+        super().__init__()
+        self.norm_final = nn.LayerNorm(hidden_size, elementwise_affine=False, eps=1e-6)
+        self.linear = nn.Linear(hidden_size, patch_size * patch_size * out_channels, bias=True)
+        self.adaLN_modulation = nn.Sequential(
+            nn.SiLU(),
+            nn.Linear(hidden_size, 2 * hidden_size, bias=True)
+        )
+
+    def forward(self, x, c):
+        shift, scale = self.adaLN_modulation(c).chunk(2, dim=1)
+        x = modulate(self.norm_final(x), shift, scale)
+        x = self.linear(x)
+        return x
+
+
+class DiT(nn.Module):
+    """
+    Diffusion model with a Transformer backbone.
+    """
+    def __init__(
+        self,
+        input_size=32,
+        patch_size=2,
+        in_channels=4,
+        hidden_size=1152,
+        depth=28,
+        num_heads=16,
+        mlp_ratio=4,
+        class_dropout_prob=0.1,
+        num_classes=1000,
+        learn_sigma=True,
+    ):
+        super().__init__()
+        self.learn_sigma = learn_sigma
+        self.in_channels = in_channels
+        self.out_channels = in_channels * 2 if learn_sigma else in_channels
+        self.patch_size = patch_size
+        self.num_heads = num_heads
+
+        self.x_embedder = PatchEmbed(input_size, patch_size, in_channels, hidden_size, bias=True)
+        self.t_embedder = TimestepEmbedder(hidden_size)
+        self.y_embedder = LabelEmbedder(num_classes, hidden_size, class_dropout_prob)
+        num_patches = self.x_embedder.num_patches
+        # Will use fixed sin-cos embedding:
+        self.pos_embed = nn.Parameter(torch.zeros(1, num_patches, hidden_size), requires_grad=False)
+
+        self.blocks = nn.ModuleList([
+            DiTBlock(hidden_size, num_heads, mlp_ratio=mlp_ratio) for _ in range(depth)
+        ])
+        self.final_layer = FinalLayer(hidden_size, patch_size, self.out_channels)
+        self.initialize_weights()
+
+    def initialize_weights(self):
+        # Initialize transformer layers:
+        def _basic_init(module):
+            if isinstance(module, nn.Linear):
+                torch.nn.init.xavier_uniform_(module.weight)
+                if module.bias is not None:
+                    nn.init.constant_(module.bias, 0)
+        self.apply(_basic_init)
+
+        # Initialize (and freeze) pos_embed by sin-cos embedding:
+        pos_embed = get_2d_sincos_pos_embed(self.pos_embed.shape[-1], int(self.x_embedder.num_patches ** 0.5))
+        self.pos_embed.data.copy_(torch.from_numpy(pos_embed).float().unsqueeze(0))
+
+        # Initialize patch_embed like nn.Linear (instead of nn.Conv2d):
+        w = self.x_embedder.proj.weight.data
+        nn.init.xavier_uniform_(w.view([w.shape[0], -1]))
+        nn.init.constant_(self.x_embedder.proj.bias, 0)
+
+        # Initialize label embedding table:
+        nn.init.normal_(self.y_embedder.embedding_table.weight, std=0.02)
+
+        # Initialize timestep embedding MLP:
+        nn.init.normal_(self.t_embedder.mlp[0].weight, std=0.02)
+        nn.init.normal_(self.t_embedder.mlp[2].weight, std=0.02)
+
+        # Zero-out adaLN modulation layers in DiT blocks:
+        for block in self.blocks:
+            nn.init.constant_(block.adaLN_modulation[-1].weight, 0)
+            nn.init.constant_(block.adaLN_modulation[-1].bias, 0)
+
+        # Zero-out output layers:
+        nn.init.constant_(self.final_layer.adaLN_modulation[-1].weight, 0)
+        nn.init.constant_(self.final_layer.adaLN_modulation[-1].bias, 0)
+        nn.init.constant_(self.final_layer.linear.weight, 0)
+        nn.init.constant_(self.final_layer.linear.bias, 0)
+
+    def unpatchify(self, x):
+        """
+        x: (N, T, patch_size**2 * C)
+        imgs: (N, H, W, C)
+        """
+        c = self.out_channels
+        p = self.x_embedder.patch_size[0]
+        h = w = int(x.shape[1] ** 0.5)
+        assert h * w == x.shape[1]
+
+        x = x.reshape(shape=(x.shape[0], h, w, p, p, c))
+        x = torch.einsum('nhwpqc->nchpwq', x)
+        imgs = x.reshape(shape=(x.shape[0], c, h * p, h * p))
+        return imgs
+
+    def forward(self, x, t, y):
+        """
+        Forward pass of DiT.
+        x: (N, C, H, W) tensor of spatial inputs (images or latent representations of images)
+        t: (N,) tensor of diffusion timesteps
+        y: (N,) tensor of class labels
+        """
+        x = self.x_embedder(x) + self.pos_embed  # (N, T, D), where T = H * W / patch_size ** 2
+        t = self.t_embedder(t)                   # (N, D)
+        y = self.y_embedder(y, self.training)    # (N, D)
+        c = t + y                                # (N, D)
+        for block in self.blocks:
+            x = block(x, c)                      # (N, T, D)
+        x = self.final_layer(x, c)                # (N, T, patch_size ** 2 * out_channels)
+        x = self.unpatchify(x)                   # (N, out_channels, H, W)
+        return x
+
+    def forward_with_cfg(self, x, t, y, cfg_scale):
+        """
+        Forward pass of DiT, but also batches the unconditional forward pass for classifier-free guidance.
+        """
+        # https://github.com/openai/glide-text2im/blob/main/notebooks/text2im.ipynb
+        half = x[: len(x) // 2]
+        combined = torch.cat([half, half], dim=0)
+        model_out = self.forward(combined, t, y)
+        # For exact reproducibility reasons, we apply classifier-free guidance on only
+        # three channels by default. The standard approach to cfg applies it to all channels.
+        # This can be done by uncommenting the following line and commenting-out the line following that.
+        # eps, rest = model_out[:, :self.in_channels], model_out[:, self.in_channels:]
+        eps, rest = model_out[:, :3], model_out[:, 3:]
+        cond_eps, uncond_eps = torch.split(eps, len(eps) // 2, dim=0)
+        half_eps = uncond_eps + cfg_scale * (cond_eps - uncond_eps)
+        eps = torch.cat([half_eps, half_eps], dim=0)
+        return torch.cat([eps, rest], dim=1)
+
+
+#################################################################################
+#                   Sine/Cosine Positional Embedding Functions                  #
+#################################################################################
+# https://github.com/facebookresearch/mae/blob/main/util/pos_embed.py
+
+def get_2d_sincos_pos_embed(embed_dim, grid_size, cls_token=False, extra_tokens=0):
+    """
+    grid_size: int of the grid height and width
+    return:
+    pos_embed: [grid_size*grid_size, embed_dim] or [1+grid_size*grid_size, embed_dim] (w/ or w/o cls_token)
+    """
+    grid_h = np.arange(grid_size, dtype=np.float32)
+    grid_w = np.arange(grid_size, dtype=np.float32)
+    grid = np.meshgrid(grid_w, grid_h)  # here w goes first
+    grid = np.stack(grid, axis=0)
+
+    grid = grid.reshape([2, 1, grid_size, grid_size])
+    pos_embed = get_2d_sincos_pos_embed_from_grid(embed_dim, grid)
+    if cls_token and extra_tokens > 0:
+        pos_embed = np.concatenate([np.zeros([extra_tokens, embed_dim]), pos_embed], axis=0)
+    return pos_embed
+
+
+def get_2d_sincos_pos_embed_from_grid(embed_dim, grid):
+    assert embed_dim % 2 == 0
+
+    # use half of dimensions to encode grid_h
+    emb_h = get_1d_sincos_pos_embed_from_grid(embed_dim // 2, grid[0])  # (H*W, D/2)
+    emb_w = get_1d_sincos_pos_embed_from_grid(embed_dim // 2, grid[1])  # (H*W, D/2)
+
+    emb = np.concatenate([emb_h, emb_w], axis=1) # (H*W, D)
+    return emb
+
+
+def get_1d_sincos_pos_embed_from_grid(embed_dim, pos):
+    """
+    embed_dim: output dimension for each position
+    pos: a list of positions to be encoded: size (M,)
+    out: (M, D)
+    """
+    assert embed_dim % 2 == 0
+    omega = np.arange(embed_dim // 2, dtype=np.float64)
+    omega /= embed_dim / 2.
+    omega = 1. / 10000**omega  # (D/2,)
+
+    pos = pos.reshape(-1)  # (M,)
+    out = np.einsum('m,d->md', pos, omega)  # (M, D/2), outer product
+
+    emb_sin = np.sin(out) # (M, D/2)
+    emb_cos = np.cos(out) # (M, D/2)
+
+    emb = np.concatenate([emb_sin, emb_cos], axis=1)  # (M, D)
+    return emb
+
+
+#################################################################################
+#                                   DiT Configs                                  #
+#################################################################################
+
+def DiT_XL_2(**kwargs):
+    return DiT(depth=28, hidden_size=1152, patch_size=2, num_heads=16, **kwargs)
+
+def DiT_XL_4(**kwargs):
+    return DiT(depth=28, hidden_size=1152, patch_size=4, num_heads=16, **kwargs)
+
+def DiT_XL_8(**kwargs):
+    return DiT(depth=28, hidden_size=1152, patch_size=8, num_heads=16, **kwargs)
+
+def DiT_L_2(**kwargs):
+    return DiT(depth=24, hidden_size=1024, patch_size=2, num_heads=16, **kwargs)
+
+def DiT_L_4(**kwargs):
+    return DiT(depth=24, hidden_size=1024, patch_size=4, num_heads=16, **kwargs)
+
+def DiT_L_8(**kwargs):
+    return DiT(depth=24, hidden_size=1024, patch_size=8, num_heads=16, **kwargs)
+
+def DiT_B_2(**kwargs):
+    return DiT(depth=12, hidden_size=768, patch_size=2, num_heads=12, **kwargs)
+
+def DiT_B_4(**kwargs):
+    return DiT(depth=12, hidden_size=768, patch_size=4, num_heads=12, **kwargs)
+
+def DiT_B_8(**kwargs):
+    return DiT(depth=12, hidden_size=768, patch_size=8, num_heads=12, **kwargs)
+
+def DiT_S_2(**kwargs):
+    return DiT(depth=12, hidden_size=384, patch_size=2, num_heads=6, **kwargs)
+
+def DiT_S_4(**kwargs):
+    return DiT(depth=12, hidden_size=384, patch_size=4, num_heads=6, **kwargs)
+
+def DiT_S_8(**kwargs):
+    return DiT(depth=12, hidden_size=384, patch_size=8, num_heads=6, **kwargs)
+
+
+DiT_models = {
+    'DiT-XL/2': DiT_XL_2,  'DiT-XL/4': DiT_XL_4,  'DiT-XL/8': DiT_XL_8,
+    'DiT-L/2':  DiT_L_2,   'DiT-L/4':  DiT_L_4,   'DiT-L/8':  DiT_L_8,
+    'DiT-B/2':  DiT_B_2,   'DiT-B/4':  DiT_B_4,   'DiT-B/8':  DiT_B_8,
+    'DiT-S/2':  DiT_S_2,   'DiT-S/4':  DiT_S_4,   'DiT-S/8':  DiT_S_8,
+}

sample.py

@@ -0,0 +1,91 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+"""
+Sample new images from a pre-trained DiT.
+"""
+import torch
+torch.backends.cuda.matmul.allow_tf32 = True
+torch.backends.cudnn.allow_tf32 = True
+from torchvision.utils import save_image
+from diffusion import create_diffusion
+from diffusers.models import AutoencoderKL
+from download import find_model
+from models import DiT_models
+import argparse
+
+
+def main(args):
+    # Setup PyTorch:
+    torch.manual_seed(args.seed)
+    torch.set_grad_enabled(False)
+    device = "cuda" if torch.cuda.is_available() else "cpu"
+
+    if args.ckpt is None:
+        # assert args.model == "DiT-XL/2", "Only DiT-XL/2 models are available for auto-download."
+        assert args.image_size in [256, 512]
+        assert args.num_classes == 1000
+
+    # Load model:
+    latent_size = args.image_size // 8
+    model = DiT_models[args.model](
+        input_size=latent_size,
+        num_classes=args.num_classes
+    ).to(device)
+    # Auto-download a pre-trained model or load a custom DiT checkpoint from train.py:
+    
+    if args.model == "DiT-S/2":
+        ckpt_path = "results/002-DiT-S-2/checkpoints/0600000.pt" 
+    else:
+        ckpt_path = "results/000-DiT-L-2/checkpoints/0550000.pt" 
+
+    state_dict = find_model(ckpt_path)
+    model.load_state_dict(state_dict)
+    model.eval()  # important!
+    diffusion = create_diffusion(str(args.num_sampling_steps))
+    vae_path = '/maindata/data/shared/multimodal/zhengcong.fei/ckpts/sd-vae-ft-mse'
+    vae = AutoencoderKL.from_pretrained(vae_path).to(device) 
+
+    # Labels to condition the model with (feel free to change):
+    class_labels = [207, 360, 387, 974, 88, 979, 417, 279]
+
+    # Create sampling noise:
+    n = len(class_labels)
+    z = torch.randn(n, 4, latent_size, latent_size, device=device)
+    y = torch.tensor(class_labels, device=device)
+
+    # Setup classifier-free guidance:
+    z = torch.cat([z, z], 0)
+    y_null = torch.tensor([1000] * n, device=device)
+    y = torch.cat([y, y_null], 0)
+    model_kwargs = dict(y=y, cfg_scale=args.cfg_scale)
+
+    # Sample images:
+    samples = diffusion.p_sample_loop(
+        model.forward_with_cfg, z.shape, z, clip_denoised=False, model_kwargs=model_kwargs, progress=True, device=device
+    )
+    samples, _ = samples.chunk(2, dim=0)  # Remove null class samples
+    samples = vae.decode(samples / 0.18215).sample
+
+    # Save and display images: 
+    if args.model == "DiT-S/2":
+        save_image(samples, "sample_s.png", nrow=4, normalize=True, value_range=(-1, 1))
+    else:
+        save_image(samples, "sample_l.png", nrow=4, normalize=True, value_range=(-1, 1))
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--model", type=str, choices=list(DiT_models.keys()), default="DiT-S/2")
+    parser.add_argument("--vae", type=str, choices=["ema", "mse"], default="mse")
+    parser.add_argument("--image-size", type=int, choices=[256, 512], default=256)
+    parser.add_argument("--num-classes", type=int, default=1000)
+    parser.add_argument("--cfg-scale", type=float, default=4.0)
+    parser.add_argument("--num-sampling-steps", type=int, default=250)
+    parser.add_argument("--seed", type=int, default=1234)
+    parser.add_argument("--ckpt", type=str, default=None,
+                        help="Optional path to a DiT checkpoint (default: auto-download a pre-trained DiT-XL/2 model).")
+    args = parser.parse_args()
+    main(args)

train.py

@@ -0,0 +1,274 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+
+"""
+A minimal training script for DiT using PyTorch DDP.
+"""
+import torch
+# the first flag below was False when we tested this script but True makes A100 training a lot faster:
+torch.backends.cuda.matmul.allow_tf32 = True
+torch.backends.cudnn.allow_tf32 = True
+import torch.distributed as dist
+from torch.nn.parallel import DistributedDataParallel as DDP
+from torch.utils.data import DataLoader
+from torch.utils.data.distributed import DistributedSampler
+from torchvision.datasets import ImageFolder
+from torchvision import transforms
+import numpy as np
+from collections import OrderedDict
+from PIL import Image
+from copy import deepcopy
+from glob import glob
+from time import time
+import argparse
+import logging
+import os
+
+from models import DiT_models
+from diffusion import create_diffusion
+from diffusers.models import AutoencoderKL
+
+
+#################################################################################
+#                             Training Helper Functions                         #
+#################################################################################
+
+@torch.no_grad()
+def update_ema(ema_model, model, decay=0.9999):
+    """
+    Step the EMA model towards the current model.
+    """
+    ema_params = OrderedDict(ema_model.named_parameters())
+    model_params = OrderedDict(model.named_parameters())
+
+    for name, param in model_params.items():
+        # TODO: Consider applying only to params that require_grad to avoid small numerical changes of pos_embed
+        ema_params[name].mul_(decay).add_(param.data, alpha=1 - decay)
+
+
+def requires_grad(model, flag=True):
+    """
+    Set requires_grad flag for all parameters in a model.
+    """
+    for p in model.parameters():
+        p.requires_grad = flag
+
+
+def cleanup():
+    """
+    End DDP training.
+    """
+    dist.destroy_process_group()
+
+
+def create_logger(logging_dir):
+    """
+    Create a logger that writes to a log file and stdout.
+    """
+    if dist.get_rank() == 0:  # real logger
+        logging.basicConfig(
+            level=logging.INFO,
+            format='[\033[34m%(asctime)s\033[0m] %(message)s',
+            datefmt='%Y-%m-%d %H:%M:%S',
+            handlers=[logging.StreamHandler(), logging.FileHandler(f"{logging_dir}/log.txt")]
+        )
+        logger = logging.getLogger(__name__)
+    else:  # dummy logger (does nothing)
+        logger = logging.getLogger(__name__)
+        logger.addHandler(logging.NullHandler())
+    return logger
+
+
+def center_crop_arr(pil_image, image_size):
+    """
+    Center cropping implementation from ADM.
+    https://github.com/openai/guided-diffusion/blob/8fb3ad9197f16bbc40620447b2742e13458d2831/guided_diffusion/image_datasets.py#L126
+    """
+    while min(*pil_image.size) >= 2 * image_size:
+        pil_image = pil_image.resize(
+            tuple(x // 2 for x in pil_image.size), resample=Image.BOX
+        )
+
+    scale = image_size / min(*pil_image.size)
+    pil_image = pil_image.resize(
+        tuple(round(x * scale) for x in pil_image.size), resample=Image.BICUBIC
+    )
+
+    arr = np.array(pil_image)
+    crop_y = (arr.shape[0] - image_size) // 2
+    crop_x = (arr.shape[1] - image_size) // 2
+    return Image.fromarray(arr[crop_y: crop_y + image_size, crop_x: crop_x + image_size])
+
+
+#################################################################################
+#                                  Training Loop                                #
+#################################################################################
+
+def main(args):
+    """
+    Trains a new DiT model.
+    """
+    assert torch.cuda.is_available(), "Training currently requires at least one GPU."
+
+    # Setup DDP:
+    dist.init_process_group("nccl")
+    assert args.global_batch_size % dist.get_world_size() == 0, f"Batch size must be divisible by world size."
+    rank = dist.get_rank()
+    device = rank % torch.cuda.device_count()
+    seed = args.global_seed * dist.get_world_size() + rank
+    torch.manual_seed(seed)
+    torch.cuda.set_device(device)
+    print(f"Starting rank={rank}, seed={seed}, world_size={dist.get_world_size()}.")
+
+    # Setup an experiment folder:
+    if rank == 0:
+        os.makedirs(args.results_dir, exist_ok=True)  # Make results folder (holds all experiment subfolders)
+        experiment_index = len(glob(f"{args.results_dir}/*"))
+        model_string_name = args.model.replace("/", "-")  # e.g., DiT-XL/2 --> DiT-XL-2 (for naming folders)
+        experiment_dir = f"{args.results_dir}/{experiment_index:03d}-{model_string_name}"  # Create an experiment folder
+        checkpoint_dir = f"{experiment_dir}/checkpoints"  # Stores saved model checkpoints
+        os.makedirs(checkpoint_dir, exist_ok=True)
+        logger = create_logger(experiment_dir)
+        logger.info(f"Experiment directory created at {experiment_dir}")
+    else:
+        logger = create_logger(None)
+
+    # Create model:
+    assert args.image_size % 8 == 0, "Image size must be divisible by 8 (for the VAE encoder)."
+    latent_size = args.image_size // 8
+    model = DiT_models[args.model](
+        input_size=latent_size,
+        num_classes=args.num_classes
+    )
+    # Note that parameter initialization is done within the DiT constructor
+    ema = deepcopy(model).to(device)  # Create an EMA of the model for use after training
+    requires_grad(ema, False)
+    model = DDP(model.to(device), device_ids=[rank])
+    diffusion = create_diffusion(timestep_respacing="")  # default: 1000 steps, linear noise schedule 
+    vae_path = '/maindata/data/shared/multimodal/zhengcong.fei/ckpts/sd-vae-ft-mse'
+    vae = AutoencoderKL.from_pretrained(vae_path).to(device)
+    logger.info(f"DiT Parameters: {sum(p.numel() for p in model.parameters()):,}")
+
+    # Setup optimizer (we used default Adam betas=(0.9, 0.999) and a constant learning rate of 1e-4 in our paper):
+    opt = torch.optim.AdamW(model.parameters(), lr=1e-4, weight_decay=0)
+
+    # Setup data:
+    transform = transforms.Compose([
+        transforms.Lambda(lambda pil_image: center_crop_arr(pil_image, args.image_size)),
+        transforms.RandomHorizontalFlip(),
+        transforms.ToTensor(),
+        transforms.Normalize(mean=[0.5, 0.5, 0.5], std=[0.5, 0.5, 0.5], inplace=True)
+    ])
+    dataset = ImageFolder(args.data_path, transform=transform)
+    sampler = DistributedSampler(
+        dataset,
+        num_replicas=dist.get_world_size(),
+        rank=rank,
+        shuffle=True,
+        seed=args.global_seed
+    )
+    loader = DataLoader(
+        dataset,
+        batch_size=int(args.global_batch_size // dist.get_world_size()),
+        shuffle=False,
+        sampler=sampler,
+        num_workers=args.num_workers,
+        pin_memory=True,
+        drop_last=True
+    )
+    logger.info(f"Dataset contains {len(dataset):,} images ({args.data_path})")
+
+    # Prepare models for training:
+    update_ema(ema, model.module, decay=0)  # Ensure EMA is initialized with synced weights
+    model.train()  # important! This enables embedding dropout for classifier-free guidance
+    ema.eval()  # EMA model should always be in eval mode
+
+    # Variables for monitoring/logging purposes:
+    train_steps = 0
+    log_steps = 0
+    running_loss = 0
+    start_time = time()
+
+    logger.info(f"Training for {args.epochs} epochs...")
+    for epoch in range(args.epochs):
+        sampler.set_epoch(epoch)
+        logger.info(f"Beginning epoch {epoch}...") 
+        data_iter_step = 0
+        for x, y in loader:
+            x = x.to(device)
+            y = y.to(device)
+            with torch.no_grad():
+                # Map input images to latent space + normalize latents:
+                x = vae.encode(x).latent_dist.sample().mul_(0.18215)
+            t = torch.randint(0, diffusion.num_timesteps, (x.shape[0],), device=device)
+            model_kwargs = dict(y=y)
+            loss_dict = diffusion.training_losses(model, x, t, model_kwargs)
+            loss = loss_dict["loss"].mean()
+            if (data_iter_step + 1) % args.accum_iter == 0:
+                opt.zero_grad()
+            loss.backward()
+            opt.step()
+            update_ema(ema, model.module)
+            
+            data_iter_step += 1
+            # Log loss values:
+            running_loss += loss.item()
+            log_steps += 1
+            train_steps += 1
+            if train_steps % args.log_every == 0:
+                # Measure training speed:
+                torch.cuda.synchronize()
+                end_time = time()
+                steps_per_sec = log_steps / (end_time - start_time)
+                # Reduce loss history over all processes:
+                avg_loss = torch.tensor(running_loss / log_steps, device=device)
+                dist.all_reduce(avg_loss, op=dist.ReduceOp.SUM)
+                avg_loss = avg_loss.item() / dist.get_world_size()
+                logger.info(f"(step={train_steps:07d}) Train Loss: {avg_loss:.4f}, Train Steps/Sec: {steps_per_sec:.2f}")
+                # Reset monitoring variables:
+                running_loss = 0
+                log_steps = 0
+                start_time = time()
+
+            # Save DiT checkpoint:
+            if train_steps % args.ckpt_every == 0 and train_steps > 0:
+                if rank == 0:
+                    checkpoint = {
+                        "model": model.module.state_dict(),
+                        "ema": ema.state_dict(),
+                        "opt": opt.state_dict(),
+                        "args": args
+                    }
+                    checkpoint_path = f"{checkpoint_dir}/{train_steps:07d}.pt"
+                    torch.save(checkpoint, checkpoint_path)
+                    logger.info(f"Saved checkpoint to {checkpoint_path}")
+                dist.barrier()
+
+    model.eval()  # important! This disables randomized embedding dropout
+    # do any sampling/FID calculation/etc. with ema (or model) in eval mode ...
+
+    logger.info("Done!")
+    cleanup()
+
+
+if __name__ == "__main__":
+    # Default args here will train DiT-XL/2 with the hyperparameters we used in our paper (except training iters).
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--data-path", type=str, required=True)
+    parser.add_argument("--results-dir", type=str, default="results")
+    parser.add_argument("--model", type=str, choices=list(DiT_models.keys()), default="DiT-L/2")
+    parser.add_argument("--image-size", type=int, choices=[256, 512], default=256)
+    parser.add_argument("--num-classes", type=int, default=1000)
+    parser.add_argument("--epochs", type=int, default=1400)
+    parser.add_argument("--global-batch-size", type=int, default=16)
+    parser.add_argument("--global-seed", type=int, default=0)
+    parser.add_argument("--vae", type=str, choices=["ema", "mse"], default="ema")  # Choice doesn't affect training
+    parser.add_argument("--num-workers", type=int, default=4)
+    parser.add_argument("--log-every", type=int, default=100)
+    parser.add_argument('--accum_iter', default=16, type=int,) 
+    parser.add_argument("--ckpt-every", type=int, default=50_000)
+    args = parser.parse_args()
+    main(args)

train.sh

@@ -0,0 +1,3 @@
+torchrun --nnodes=1 --nproc_per_node=8 train.py \
+--model DiT-L/2 \
+--data-path /maindata/data/shared/multimodal/public/dataset_img_only/imagenet/data/train