embeddings.py

# Copyright 2022 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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import math

import numpy as np
import torch
from torch import nn


def get_timestep_embedding(
    timesteps: torch.Tensor,
    embedding_dim: int,
    flip_sin_to_cos: bool = False,
    downscale_freq_shift: float = 1,
    scale: float = 1,
    max_period: int = 10000,
):
    """
    This matches the implementation in Denoising Diffusion Probabilistic Models: Create sinusoidal timestep embeddings.

    :param timesteps: a 1-D Tensor of N indices, one per batch element.
                      These may be fractional.
    :param embedding_dim: the dimension of the output. :param max_period: controls the minimum frequency of the
    embeddings. :return: an [N x dim] Tensor of positional embeddings.
    """
    assert len(timesteps.shape) == 1, "Timesteps should be a 1d-array"

    half_dim = embedding_dim // 2
    exponent = -math.log(max_period) * torch.arange(
        start=0, end=half_dim, dtype=torch.float32, device=timesteps.device
    )
    exponent = exponent / (half_dim - downscale_freq_shift)

    emb = torch.exp(exponent)
    emb = timesteps[:, None].float() * emb[None, :]

    # scale embeddings
    emb = scale * emb

    # concat sine and cosine embeddings
    emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim=-1)

    # flip sine and cosine embeddings
    if flip_sin_to_cos:
        emb = torch.cat([emb[:, half_dim:], emb[:, :half_dim]], dim=-1)

    # zero pad
    if embedding_dim % 2 == 1:
        emb = torch.nn.functional.pad(emb, (0, 1, 0, 0))
    return emb


class TimestepEmbedding(nn.Module):
    def __init__(self, in_channels: int, time_embed_dim: int, act_fn: str = "silu", out_dim: int = None):
        super().__init__()

        self.linear_1 = nn.Linear(in_channels, time_embed_dim)
        self.act = None
        if act_fn == "silu":
            self.act = nn.SiLU()
        elif act_fn == "mish":
            self.act = nn.Mish()

        if out_dim is not None:
            time_embed_dim_out = out_dim
        else:
            time_embed_dim_out = time_embed_dim
        self.linear_2 = nn.Linear(time_embed_dim, time_embed_dim_out)

    def forward(self, sample):
        sample = self.linear_1(sample)

        if self.act is not None:
            sample = self.act(sample)

        sample = self.linear_2(sample)
        return sample


class Timesteps(nn.Module):
    def __init__(self, num_channels: int, flip_sin_to_cos: bool, downscale_freq_shift: float):
        super().__init__()
        self.num_channels = num_channels
        self.flip_sin_to_cos = flip_sin_to_cos
        self.downscale_freq_shift = downscale_freq_shift

    def forward(self, timesteps):
        t_emb = get_timestep_embedding(
            timesteps,
            self.num_channels,
            flip_sin_to_cos=self.flip_sin_to_cos,
            downscale_freq_shift=self.downscale_freq_shift,
        )
        return t_emb


class GaussianFourierProjection(nn.Module):
    """Gaussian Fourier embeddings for noise levels."""

    def __init__(
        self, embedding_size: int = 256, scale: float = 1.0, set_W_to_weight=True, log=True, flip_sin_to_cos=False
    ):
        super().__init__()
        self.weight = nn.Parameter(torch.randn(embedding_size) * scale, requires_grad=False)
        self.log = log
        self.flip_sin_to_cos = flip_sin_to_cos

        if set_W_to_weight:
            # to delete later
            self.W = nn.Parameter(torch.randn(embedding_size) * scale, requires_grad=False)

            self.weight = self.W

    def forward(self, x):
        if self.log:
            x = torch.log(x)

        x_proj = x[:, None] * self.weight[None, :] * 2 * np.pi

        if self.flip_sin_to_cos:
            out = torch.cat([torch.cos(x_proj), torch.sin(x_proj)], dim=-1)
        else:
            out = torch.cat([torch.sin(x_proj), torch.cos(x_proj)], dim=-1)
        return out


class ImagePositionalEmbeddings(nn.Module):
    """
    Converts latent image classes into vector embeddings. Sums the vector embeddings with positional embeddings for the
    height and width of the latent space.

    For more details, see figure 10 of the dall-e paper: https://arxiv.org/abs/2102.12092

    For VQ-diffusion:

    Output vector embeddings are used as input for the transformer.

    Note that the vector embeddings for the transformer are different than the vector embeddings from the VQVAE.

    Args:
        num_embed (`int`):
            Number of embeddings for the latent pixels embeddings.
        height (`int`):
            Height of the latent image i.e. the number of height embeddings.
        width (`int`):
            Width of the latent image i.e. the number of width embeddings.
        embed_dim (`int`):
            Dimension of the produced vector embeddings. Used for the latent pixel, height, and width embeddings.
    """

    def __init__(
        self,
        num_embed: int,
        height: int,
        width: int,
        embed_dim: int,
    ):
        super().__init__()

        self.height = height
        self.width = width
        self.num_embed = num_embed
        self.embed_dim = embed_dim

        self.emb = nn.Embedding(self.num_embed, embed_dim)
        self.height_emb = nn.Embedding(self.height, embed_dim)
        self.width_emb = nn.Embedding(self.width, embed_dim)

    def forward(self, index):
        emb = self.emb(index)

        height_emb = self.height_emb(torch.arange(self.height, device=index.device).view(1, self.height))

        # 1 x H x D -> 1 x H x 1 x D
        height_emb = height_emb.unsqueeze(2)

        width_emb = self.width_emb(torch.arange(self.width, device=index.device).view(1, self.width))

        # 1 x W x D -> 1 x 1 x W x D
        width_emb = width_emb.unsqueeze(1)

        pos_emb = height_emb + width_emb

        # 1 x H x W x D -> 1 x L xD
        pos_emb = pos_emb.view(1, self.height * self.width, -1)

        emb = emb + pos_emb[:, : emb.shape[1], :]

        return emb