ldm/modules/diffusionmodules/util.py

# adopted from
# https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
# and
# https://github.com/lucidrains/denoising-diffusion-pytorch/blob/7706bdfc6f527f58d33f84b7b522e61e6e3164b3/denoising_diffusion_pytorch/denoising_diffusion_pytorch.py
# and
# https://github.com/openai/guided-diffusion/blob/0ba878e517b276c45d1195eb29f6f5f72659a05b/guided_diffusion/nn.py
#
# thanks!


import os
import math
import torch
import torch.nn as nn
import numpy as np
from einops import repeat
import warnings
from ldm.util import instantiate_from_config


def make_beta_schedule(schedule, n_timestep, linear_start=1e-4, linear_end=2e-2, cosine_s=8e-3):
    if schedule == "linear":
        betas = (
                torch.linspace(linear_start ** 0.5, linear_end ** 0.5, n_timestep, dtype=torch.float64) ** 2
        )

    elif schedule == "cosine":
        timesteps = (
                torch.arange(n_timestep + 1, dtype=torch.float64) / n_timestep + cosine_s
        )
        alphas = timesteps / (1 + cosine_s) * np.pi / 2
        alphas = torch.cos(alphas).pow(2)
        alphas = alphas / alphas[0]
        betas = 1 - alphas[1:] / alphas[:-1]
        betas = np.clip(betas, a_min=0, a_max=0.999)

    elif schedule == "sqrt_linear":
        betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64)
    elif schedule == "sqrt":
        betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64) ** 0.5
    else:
        raise ValueError(f"schedule '{schedule}' unknown.")
    return betas.numpy()


def make_ddim_timesteps(ddim_discr_method, num_ddim_timesteps, num_ddpm_timesteps, verbose=True):
    if ddim_discr_method == 'uniform':
        c = num_ddpm_timesteps // num_ddim_timesteps
        ddim_timesteps = np.asarray(list(range(0, num_ddpm_timesteps, c)))
    elif ddim_discr_method == 'quad':
        ddim_timesteps = ((np.linspace(0, np.sqrt(num_ddpm_timesteps * .8), num_ddim_timesteps)) ** 2).astype(int)
    else:
        raise NotImplementedError(f'There is no ddim discretization method called "{ddim_discr_method}"')

    # assert ddim_timesteps.shape[0] == num_ddim_timesteps
    # add one to get the final alpha values right (the ones from first scale to data during sampling)
    steps_out = ddim_timesteps + 1
    if verbose:
        print(f'Selected timesteps for ddim sampler: {steps_out}')
    return steps_out


def make_ddim_sampling_parameters(alphacums, ddim_timesteps, eta, verbose=True):
    # select alphas for computing the variance schedule
    alphas = alphacums[ddim_timesteps]
    alphas_prev = np.asarray([alphacums[0]] + alphacums[ddim_timesteps[:-1]].tolist())

    # according the the formula provided in https://arxiv.org/abs/2010.02502
    sigmas = eta * np.sqrt((1 - alphas_prev) / (1 - alphas) * (1 - alphas / alphas_prev))
    if verbose:
        print(f'Selected alphas for ddim sampler: a_t: {alphas}; a_(t-1): {alphas_prev}')
        print(f'For the chosen value of eta, which is {eta}, '
              f'this results in the following sigma_t schedule for ddim sampler {sigmas}')
    return sigmas, alphas, alphas_prev


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)


def extract_into_tensor(a, t, x_shape):
    b, *_ = t.shape
    out = a.gather(-1, t)
    return out.reshape(b, *((1,) * (len(x_shape) - 1)))


def checkpoint(func, inputs, params, flag):
    """

    Evaluate a function without caching intermediate activations, allowing for

    reduced memory at the expense of extra compute in the backward pass.

    :param func: the function to evaluate.

    :param inputs: the argument sequence to pass to `func`.

    :param params: a sequence of parameters `func` depends on but does not

                   explicitly take as arguments.

    :param flag: if False, disable gradient checkpointing.

    """
    if flag:
        args = tuple(inputs) + tuple(params)
        return CheckpointFunction.apply(func, len(inputs), *args)
    else:
        return func(*inputs)


class CheckpointFunction(torch.autograd.Function):
    @staticmethod
    def forward(ctx, run_function, length, *args):
        ctx.run_function = run_function
        ctx.input_tensors = list(args[:length])
        ctx.input_params = list(args[length:])

        with torch.no_grad():
            output_tensors = ctx.run_function(*ctx.input_tensors)
        return output_tensors

    @staticmethod
    def backward(ctx, *output_grads):
        ctx.input_tensors = [x.detach().requires_grad_(True) for x in ctx.input_tensors]
        with torch.enable_grad():
            # Fixes a bug where the first op in run_function modifies the
            # Tensor storage in place, which is not allowed for detach()'d
            # Tensors.
            shallow_copies = [x.view_as(x) for x in ctx.input_tensors]
            output_tensors = ctx.run_function(*shallow_copies)
        input_grads = torch.autograd.grad(
            output_tensors,
            ctx.input_tensors + ctx.input_params,
            output_grads,
            allow_unused=True,
        )
        del ctx.input_tensors
        del ctx.input_params
        del output_tensors
        return (None, None) + input_grads


def timestep_embedding(timesteps, dim, max_period=10000, repeat_only=False):
    """

    Create sinusoidal timestep embeddings.

    :param timesteps: 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 x dim] Tensor of positional embeddings.

    """
    if not repeat_only:
        half = dim // 2
        freqs = torch.exp(
            -math.log(max_period) * torch.arange(start=0, end=half, dtype=torch.float32) / half
        ).to(device=timesteps.device) # [dim//2]
        args = timesteps[:, None].float() * freqs[None] # [N,dim//2]
        embedding = torch.cat([torch.cos(args), torch.sin(args)], dim=-1) # [N,dim]
        if dim % 2:
            embedding = torch.cat([embedding, torch.zeros_like(embedding[:, :1])], dim=-1)
    else:
        embedding = repeat(timesteps, 'b -> b d', d=dim)
    return embedding


def zero_module(module):
    """

    Zero out the parameters of a module and return it.

    """
    for p in module.parameters():
        p.detach().zero_()
    return module


def scale_module(module, scale):
    """

    Scale the parameters of a module and return it.

    """
    for p in module.parameters():
        p.detach().mul_(scale)
    return module


def mean_flat(tensor):
    """

    Take the mean over all non-batch dimensions.

    """
    return tensor.mean(dim=list(range(1, len(tensor.shape))))


def normalization(channels):
    """

    Make a standard normalization layer.

    :param channels: number of input channels.

    :return: an nn.Module for normalization.

    """
    return GroupNorm32(32, channels)


# PyTorch 1.7 has SiLU, but we support PyTorch 1.5.
class SiLU(nn.Module):
    def forward(self, x):
        return x * torch.sigmoid(x)


class GroupNorm32(nn.GroupNorm):
    def forward(self, x):
        return super().forward(x.float()).type(x.dtype)

def conv_nd(dims, *args, **kwargs):
    """

    Create a 1D, 2D, or 3D convolution module.

    """
    if dims == 1:
        return nn.Conv1d(*args, **kwargs)
    elif dims == 2:
        return nn.Conv2d(*args, **kwargs)
    elif dims == 3:
        return nn.Conv3d(*args, **kwargs)
    raise ValueError(f"unsupported dimensions: {dims}")


def linear(*args, **kwargs):
    """

    Create a linear module.

    """
    return nn.Linear(*args, **kwargs)


def avg_pool_nd(dims, *args, **kwargs):
    """

    Create a 1D, 2D, or 3D average pooling module.

    """
    if dims == 1:
        return nn.AvgPool1d(*args, **kwargs)
    elif dims == 2:
        return nn.AvgPool2d(*args, **kwargs)
    elif dims == 3:
        return nn.AvgPool3d(*args, **kwargs)
    raise ValueError(f"unsupported dimensions: {dims}")


class HybridConditioner(nn.Module):

    def __init__(self, c_concat_config, c_crossattn_config):
        super().__init__()
        self.concat_conditioner = instantiate_from_config(c_concat_config)
        self.crossattn_conditioner = instantiate_from_config(c_crossattn_config)

    def forward(self, c_concat, c_crossattn):
        c_concat = self.concat_conditioner(c_concat)
        c_crossattn = self.crossattn_conditioner(c_crossattn)
        return {'c_concat': [c_concat], 'c_crossattn': [c_crossattn]}


def noise_like(shape, device, repeat=False):
    repeat_noise = lambda: torch.randn((1, *shape[1:]), device=device).repeat(shape[0], *((1,) * (len(shape) - 1)))
    noise = lambda: torch.randn(shape, device=device)
    return repeat_noise() if repeat else noise()

def _no_grad_trunc_normal_(tensor, mean, std, a, b):
    # Cut & paste from PyTorch official master until it's in a few official releases - RW
    # Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
    def norm_cdf(x):
        # Computes standard normal cumulative distribution function
        return (1. + math.erf(x / math.sqrt(2.))) / 2.

    if (mean < a - 2 * std) or (mean > b + 2 * std):
        warnings.warn("mean is more than 2 std from [a, b] in nn.init.trunc_normal_. "
                      "The distribution of values may be incorrect.",
                      stacklevel=2)

    with torch.no_grad():
        # Values are generated by using a truncated uniform distribution and
        # then using the inverse CDF for the normal distribution.
        # Get upper and lower cdf values
        l = norm_cdf((a - mean) / std)
        u = norm_cdf((b - mean) / std)

        # Uniformly fill tensor with values from [l, u], then translate to
        # [2l-1, 2u-1].
        tensor.uniform_(2 * l - 1, 2 * u - 1)

        # Use inverse cdf transform for normal distribution to get truncated
        # standard normal
        tensor.erfinv_()

        # Transform to proper mean, std
        tensor.mul_(std * math.sqrt(2.))
        tensor.add_(mean)

        # Clamp to ensure it's in the proper range
        tensor.clamp_(min=a, max=b)
        return tensor


def trunc_normal_(tensor, mean=0., std=1., a=-2., b=2.):
    r"""Fills the input Tensor with values drawn from a truncated

    normal distribution. The values are effectively drawn from the

    normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`

    with values outside :math:`[a, b]` redrawn until they are within

    the bounds. The method used for generating the random values works

    best when :math:`a \leq \text{mean} \leq b`.

    Args:

        tensor: an n-dimensional `torch.Tensor`

        mean: the mean of the normal distribution

        std: the standard deviation of the normal distribution

        a: the minimum cutoff value

        b: the maximum cutoff value

    Examples:

        >>> w = torch.empty(3, 5)

        >>> nn.init.trunc_normal_(w)

    """
    return _no_grad_trunc_normal_(tensor, mean, std, a, b)