enso/models.py

# 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

try:
    import flash_attn
    if hasattr(flash_attn, '__version__') and int(flash_attn.__version__[0]) == 2:
        from flash_attn.flash_attn_interface import flash_attn_kvpacked_func
        from flash_attn.modules.mha import FlashSelfAttention 
    else:
        from flash_attn.flash_attn_interface import flash_attn_unpadded_kvpacked_func
        from flash_attn.modules.mha import FlashSelfAttention
except Exception as e:
    print(f'flash_attn import failed: {e}')



# selected_ids_list = []



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)
        # if inference with fp16, embedding.half()
        return embedding 

    def forward(self, t):
        t_freq = self.timestep_embedding(t, self.frequency_embedding_size) 
        t_emb = self.mlp(t_freq)#.half())
        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    
        # print(bsz, seq_len, h)    
        ### 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, pretraining_tp=2):
        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 = pretraining_tp

    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) 
            # print(self.up_proj.weight.size(), self.down_proj.weight.size())
            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, pretraining_tp=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, pretraining_tp=pretraining_tp) 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, pretraining_tp=pretraining_tp)
    
    def forward(self, hidden_states):
        identity = hidden_states
        orig_shape = hidden_states.shape
        topk_idx, topk_weight, aux_loss = self.gate(hidden_states) 
        # print(topk_idx.tolist(), print(len(topk_idx.tolist()))) 
        # global selected_ids_list
        # selected_ids_list.append(topk_idx.tolist())

        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, dtype=hidden_states.dtype)
            for i, expert in enumerate(self.experts): 
                y[flat_topk_idx == i] = expert(hidden_states[flat_topk_idx == i]).float()
            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)




#################################################################################
#                              Flash attention Layer.                           #
#################################################################################

class FlashSelfMHAModified(nn.Module):
    """
    self-attention with flashattention
    """
    def __init__(self,
                 dim,
                 num_heads,
                 qkv_bias=True,
                 qk_norm=False,
                 attn_drop=0.0,
                 proj_drop=0.0,
                 device=None,
                 dtype=None,
                 norm_layer=nn.LayerNorm,
                 ):
        factory_kwargs = {'device': device, 'dtype': dtype}
        super().__init__()
        self.dim = dim
        self.num_heads = num_heads
        assert self.dim % num_heads == 0, "self.kdim must be divisible by num_heads"
        self.head_dim = self.dim // num_heads
        assert self.head_dim % 8 == 0 and self.head_dim <= 128, "Only support head_dim <= 128 and divisible by 8"

        self.Wqkv = nn.Linear(dim, 3 * dim, bias=qkv_bias, **factory_kwargs)
        # TODO: eps should be 1 / 65530 if using fp16
        self.q_norm = norm_layer(self.head_dim, elementwise_affine=True, eps=1e-6) if qk_norm else nn.Identity()
        self.k_norm = norm_layer(self.head_dim, elementwise_affine=True, eps=1e-6) if qk_norm else nn.Identity()
        self.inner_attn = FlashSelfAttention(attention_dropout=attn_drop)
        self.out_proj = nn.Linear(dim, dim, bias=qkv_bias, **factory_kwargs)
        self.proj_drop = nn.Dropout(proj_drop)

    def forward(self, x,):
        """
        Parameters
        ----------
        x: torch.Tensor
            (batch, seqlen, hidden_dim) (where hidden_dim = num heads * head dim)
        """
        b, s, d = x.shape

        qkv = self.Wqkv(x)
        qkv = qkv.view(b, s, 3, self.num_heads, self.head_dim)  # [b, s, 3, h, d]
        q, k, v = qkv.unbind(dim=2) # [b, s, h, d]
        q = self.q_norm(q).half()   # [b, s, h, d]
        k = self.k_norm(k).half()

        qkv = torch.stack([q, k, v], dim=2)     # [b, s, 3, h, d]
        context = self.inner_attn(qkv)
        out = self.out_proj(context.view(b, s, d))
        out = self.proj_drop(out)

        return out


#################################################################################
#                                 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, pretraining_tp=2, 
        use_flash_attn=False, **block_kwargs
    ):
        super().__init__()
        self.norm1 = nn.LayerNorm(hidden_size, elementwise_affine=False, eps=1e-6)
        if use_flash_attn: 
            self.attn = FlashSelfMHAModified(hidden_size, num_heads=num_heads, qkv_bias=True, qk_norm=True)
        else:
            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, pretraining_tp)

        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,
        num_experts=8, num_experts_per_tok=2,
        pretraining_tp=2,
        learn_sigma=True,
        use_flash_attn=False,
    ):
        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, num_experts, num_experts_per_tok, pretraining_tp, use_flash_attn) 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 = x.half()
        # t = t.half()
        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_G_2(**kwargs):
    return DiT(depth=40, hidden_size=1408, patch_size=2, num_heads=16, **kwargs)

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,
    'DiT-G/2': DiT_G_2,
}