diffusion/model/edm_sample.py

# Copyright 2024 NVIDIA CORPORATION & AFFILIATES
#
# 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.
#
# SPDX-License-Identifier: Apache-2.0

# Modified from OpenAI's diffusion repos
#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py

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