import math
import numpy as np
import torch
import torch.nn.functional as F
from einops import repeat
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 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)))
steps_out = ddim_timesteps + 1
elif ddim_discr_method == 'uniform_trailing':
c = num_ddpm_timesteps / num_ddim_timesteps
ddim_timesteps = np.flip(np.round(np.arange(num_ddpm_timesteps, 0, -c))).astype(np.int64)
steps_out = ddim_timesteps - 1
elif ddim_discr_method == 'quad':
ddim_timesteps = ((np.linspace(0, np.sqrt(num_ddpm_timesteps * .8), num_ddim_timesteps)) ** 2).astype(int)
steps_out = ddim_timesteps + 1
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
# print(f'ddim_timesteps={ddim_timesteps}, len_alphacums={len(alphacums)}')
alphas = alphacums[ddim_timesteps]
alphas_prev = np.asarray([alphacums[0]] + alphacums[ddim_timesteps[:-1]].tolist())
# according 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 rescale_zero_terminal_snr(betas):
"""
Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
Args:
betas (`numpy.ndarray`):
the betas that the scheduler is being initialized with.
Returns:
`numpy.ndarray`: rescaled betas with zero terminal SNR
"""
# Convert betas to alphas_bar_sqrt
alphas = 1.0 - betas
alphas_cumprod = np.cumprod(alphas, axis=0)
alphas_bar_sqrt = np.sqrt(alphas_cumprod)
# Store old values.
alphas_bar_sqrt_0 = alphas_bar_sqrt[0].copy()
alphas_bar_sqrt_T = alphas_bar_sqrt[-1].copy()
# Shift so the last timestep is zero.
alphas_bar_sqrt -= alphas_bar_sqrt_T
# Scale so the first timestep is back to the old value.
alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
# Convert alphas_bar_sqrt to betas
alphas_bar = alphas_bar_sqrt**2 # Revert sqrt
alphas = alphas_bar[1:] / alphas_bar[:-1] # Revert cumprod
alphas = np.concatenate([alphas_bar[0:1], alphas])
betas = 1 - alphas
return betas
def rescale_noise_cfg(noise_cfg, noise_pred_text, guidance_rescale=0.0):
"""
Rescale `noise_cfg` according to `guidance_rescale`. Based on findings of [Common Diffusion Noise Schedules and
Sample Steps are Flawed](https://arxiv.org/pdf/2305.08891.pdf). See Section 3.4
"""
std_text = noise_pred_text.std(dim=list(range(1, noise_pred_text.ndim)), keepdim=True)
std_cfg = noise_cfg.std(dim=list(range(1, noise_cfg.ndim)), keepdim=True)
# rescale the results from guidance (fixes overexposure)
noise_pred_rescaled = noise_cfg * (std_text / std_cfg)
# mix with the original results from guidance by factor guidance_rescale to avoid "plain looking" images
noise_cfg = guidance_rescale * noise_pred_rescaled + (1 - guidance_rescale) * noise_cfg
return noise_cfg