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,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
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, channel: int, time_embed_dim: int, act_fn: str = "silu"):
        super().__init__()

        self.linear_1 = nn.Linear(channel, time_embed_dim)
        self.act = None
        if act_fn == "silu":
            self.act = nn.SiLU()
        self.linear_2 = nn.Linear(time_embed_dim, time_embed_dim)

    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