import random
import numpy as np
from tqdm import tqdm
from diffusion.model.utils import *
# ----------------------------------------------------------------------------
# Proposed EDM sampler (Algorithm 2).
def edm_sampler(
net, latents, class_labels=None, cfg_scale=None, randn_like=torch.randn_like,
num_steps=18, sigma_min=0.002, sigma_max=80, rho=7,
S_churn=0, S_min=0, S_max=float('inf'), S_noise=1, **kwargs
):
# Adjust noise levels based on what's supported by the network.
sigma_min = max(sigma_min, net.sigma_min)
sigma_max = min(sigma_max, net.sigma_max)
# Time step discretization.
step_indices = torch.arange(num_steps, dtype=torch.float64, device=latents.device)
t_steps = (sigma_max ** (1 / rho) + step_indices / (num_steps - 1) * (
sigma_min ** (1 / rho) - sigma_max ** (1 / rho))) ** rho
t_steps = torch.cat([net.round_sigma(t_steps), torch.zeros_like(t_steps[:1])]) # t_N = 0
# Main sampling loop.
x_next = latents.to(torch.float64) * t_steps[0]
for i, (t_cur, t_next) in tqdm(list(enumerate(zip(t_steps[:-1], t_steps[1:])))): # 0, ..., N-1
x_cur = x_next
# Increase noise temporarily.
gamma = min(S_churn / num_steps, np.sqrt(2) - 1) if S_min <= t_cur <= S_max else 0
t_hat = net.round_sigma(t_cur + gamma * t_cur)
x_hat = x_cur + (t_hat ** 2 - t_cur ** 2).sqrt() * S_noise * randn_like(x_cur)
# Euler step.
denoised = net(x_hat.float(), t_hat, class_labels, cfg_scale, **kwargs)['x'].to(torch.float64)
d_cur = (x_hat - denoised) / t_hat
x_next = x_hat + (t_next - t_hat) * d_cur
# Apply 2nd order correction.
if i < num_steps - 1:
denoised = net(x_next.float(), t_next, class_labels, cfg_scale, **kwargs)['x'].to(torch.float64)
d_prime = (x_next - denoised) / t_next
x_next = x_hat + (t_next - t_hat) * (0.5 * d_cur + 0.5 * d_prime)
return x_next
# ----------------------------------------------------------------------------
# Generalized ablation sampler, representing the superset of all sampling
# methods discussed in the paper.
def ablation_sampler(
net, latents, class_labels=None, cfg_scale=None, feat=None, randn_like=torch.randn_like,
num_steps=18, sigma_min=None, sigma_max=None, rho=7,
solver='heun', discretization='edm', schedule='linear', scaling='none',
epsilon_s=1e-3, C_1=0.001, C_2=0.008, M=1000, alpha=1,
S_churn=0, S_min=0, S_max=float('inf'), S_noise=1,
):
assert solver in ['euler', 'heun']
assert discretization in ['vp', 've', 'iddpm', 'edm']
assert schedule in ['vp', 've', 'linear']
assert scaling in ['vp', 'none']
# Helper functions for VP & VE noise level schedules.
vp_sigma = lambda beta_d, beta_min: lambda t: (np.e ** (0.5 * beta_d * (t ** 2) + beta_min * t) - 1) ** 0.5
vp_sigma_deriv = lambda beta_d, beta_min: lambda t: 0.5 * (beta_min + beta_d * t) * (sigma(t) + 1 / sigma(t))
vp_sigma_inv = lambda beta_d, beta_min: lambda sigma: ((beta_min ** 2 + 2 * beta_d * (
sigma ** 2 + 1).log()).sqrt() - beta_min) / beta_d
ve_sigma = lambda t: t.sqrt()
ve_sigma_deriv = lambda t: 0.5 / t.sqrt()
ve_sigma_inv = lambda sigma: sigma ** 2
# Select default noise level range based on the specified time step discretization.
if sigma_min is None:
vp_def = vp_sigma(beta_d=19.1, beta_min=0.1)(t=epsilon_s)
sigma_min = {'vp': vp_def, 've': 0.02, 'iddpm': 0.002, 'edm': 0.002}[discretization]
if sigma_max is None:
vp_def = vp_sigma(beta_d=19.1, beta_min=0.1)(t=1)
sigma_max = {'vp': vp_def, 've': 100, 'iddpm': 81, 'edm': 80}[discretization]
# Adjust noise levels based on what's supported by the network.
sigma_min = max(sigma_min, net.sigma_min)
sigma_max = min(sigma_max, net.sigma_max)
# Compute corresponding betas for VP.
vp_beta_d = 2 * (np.log(sigma_min ** 2 + 1) / epsilon_s - np.log(sigma_max ** 2 + 1)) / (epsilon_s - 1)
vp_beta_min = np.log(sigma_max ** 2 + 1) - 0.5 * vp_beta_d
# Define time steps in terms of noise level.
step_indices = torch.arange(num_steps, dtype=torch.float64, device=latents.device)
if discretization == 'vp':
orig_t_steps = 1 + step_indices / (num_steps - 1) * (epsilon_s - 1)
sigma_steps = vp_sigma(vp_beta_d, vp_beta_min)(orig_t_steps)
elif discretization == 've':
orig_t_steps = (sigma_max ** 2) * ((sigma_min ** 2 / sigma_max ** 2) ** (step_indices / (num_steps - 1)))
sigma_steps = ve_sigma(orig_t_steps)
elif discretization == 'iddpm':
u = torch.zeros(M + 1, dtype=torch.float64, device=latents.device)
alpha_bar = lambda j: (0.5 * np.pi * j / M / (C_2 + 1)).sin() ** 2
for j in torch.arange(M, 0, -1, device=latents.device): # M, ..., 1
u[j - 1] = ((u[j] ** 2 + 1) / (alpha_bar(j - 1) / alpha_bar(j)).clip(min=C_1) - 1).sqrt()
u_filtered = u[torch.logical_and(u >= sigma_min, u <= sigma_max)]
sigma_steps = u_filtered[((len(u_filtered) - 1) / (num_steps - 1) * step_indices).round().to(torch.int64)]
else:
assert discretization == 'edm'
sigma_steps = (sigma_max ** (1 / rho) + step_indices / (num_steps - 1) * (
sigma_min ** (1 / rho) - sigma_max ** (1 / rho))) ** rho
# Define noise level schedule.
if schedule == 'vp':
sigma = vp_sigma(vp_beta_d, vp_beta_min)
sigma_deriv = vp_sigma_deriv(vp_beta_d, vp_beta_min)
sigma_inv = vp_sigma_inv(vp_beta_d, vp_beta_min)
elif schedule == 've':
sigma = ve_sigma
sigma_deriv = ve_sigma_deriv
sigma_inv = ve_sigma_inv
else:
assert schedule == 'linear'
sigma = lambda t: t
sigma_deriv = lambda t: 1
sigma_inv = lambda sigma: sigma
# Define scaling schedule.
if scaling == 'vp':
s = lambda t: 1 / (1 + sigma(t) ** 2).sqrt()
s_deriv = lambda t: -sigma(t) * sigma_deriv(t) * (s(t) ** 3)
else:
assert scaling == 'none'
s = lambda t: 1
s_deriv = lambda t: 0
# Compute final time steps based on the corresponding noise levels.
t_steps = sigma_inv(net.round_sigma(sigma_steps))
t_steps = torch.cat([t_steps, torch.zeros_like(t_steps[:1])]) # t_N = 0
# Main sampling loop.
t_next = t_steps[0]
x_next = latents.to(torch.float64) * (sigma(t_next) * s(t_next))
for i, (t_cur, t_next) in enumerate(zip(t_steps[:-1], t_steps[1:])): # 0, ..., N-1
x_cur = x_next
# Increase noise temporarily.
gamma = min(S_churn / num_steps, np.sqrt(2) - 1) if S_min <= sigma(t_cur) <= S_max else 0
t_hat = sigma_inv(net.round_sigma(sigma(t_cur) + gamma * sigma(t_cur)))
x_hat = s(t_hat) / s(t_cur) * x_cur + (sigma(t_hat) ** 2 - sigma(t_cur) ** 2).clip(min=0).sqrt() * s(
t_hat) * S_noise * randn_like(x_cur)
# Euler step.
h = t_next - t_hat
denoised = net(x_hat.float() / s(t_hat), sigma(t_hat), class_labels, cfg_scale, feat=feat)['x'].to(
torch.float64)
d_cur = (sigma_deriv(t_hat) / sigma(t_hat) + s_deriv(t_hat) / s(t_hat)) * x_hat - sigma_deriv(t_hat) * s(
t_hat) / sigma(t_hat) * denoised
x_prime = x_hat + alpha * h * d_cur
t_prime = t_hat + alpha * h
# Apply 2nd order correction.
if solver == 'euler' or i == num_steps - 1:
x_next = x_hat + h * d_cur
else:
assert solver == 'heun'
denoised = net(x_prime.float() / s(t_prime), sigma(t_prime), class_labels, cfg_scale, feat=feat)['x'].to(
torch.float64)
d_prime = (sigma_deriv(t_prime) / sigma(t_prime) + s_deriv(t_prime) / s(t_prime)) * x_prime - sigma_deriv(
t_prime) * s(t_prime) / sigma(t_prime) * denoised
x_next = x_hat + h * ((1 - 1 / (2 * alpha)) * d_cur + 1 / (2 * alpha) * d_prime)
return x_next