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# 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
from audioldm.utils 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 * 0.8), 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).contiguous()
return out.reshape(b, *((1,) * (len(x_shape) - 1))).contiguous()
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)
args = timesteps[:, 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
)
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()