diffusion/model/diffusion_utils.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 numpy as np
import torch as th


def normal_kl(mean1, logvar1, mean2, logvar2):
    """
    Compute the KL divergence between two gaussians.
    Shapes are automatically broadcasted, so batches can be compared to
    scalars, among other use cases.
    """
    tensor = None
    for obj in (mean1, logvar1, mean2, logvar2):
        if isinstance(obj, th.Tensor):
            tensor = obj
            break
    assert tensor is not None, "at least one argument must be a Tensor"

    # Force variances to be Tensors. Broadcasting helps convert scalars to
    # Tensors, but it does not work for th.exp().
    logvar1, logvar2 = (
        x if isinstance(x, th.Tensor) else th.tensor(x, device=tensor.device) for x in (logvar1, logvar2)
    )

    return 0.5 * (-1.0 + logvar2 - logvar1 + th.exp(logvar1 - logvar2) + ((mean1 - mean2) ** 2) * th.exp(-logvar2))


def approx_standard_normal_cdf(x):
    """
    A fast approximation of the cumulative distribution function of the
    standard normal.
    """
    return 0.5 * (1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3))))


def continuous_gaussian_log_likelihood(x, *, means, log_scales):
    """
    Compute the log-likelihood of a continuous Gaussian distribution.
    :param x: the targets
    :param means: the Gaussian mean Tensor.
    :param log_scales: the Gaussian log stddev Tensor.
    :return: a tensor like x of log probabilities (in nats).
    """
    centered_x = x - means
    inv_stdv = th.exp(-log_scales)
    normalized_x = centered_x * inv_stdv
    log_probs = th.distributions.Normal(th.zeros_like(x), th.ones_like(x)).log_prob(normalized_x)
    return log_probs


def discretized_gaussian_log_likelihood(x, *, means, log_scales):
    """
    Compute the log-likelihood of a Gaussian distribution discretizing to a
    given image.
    :param x: the target images. It is assumed that this was uint8 values,
              rescaled to the range [-1, 1].
    :param means: the Gaussian mean Tensor.
    :param log_scales: the Gaussian log stddev Tensor.
    :return: a tensor like x of log probabilities (in nats).
    """
    assert x.shape == means.shape == log_scales.shape
    centered_x = x - means
    inv_stdv = th.exp(-log_scales)
    plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
    cdf_plus = approx_standard_normal_cdf(plus_in)
    min_in = inv_stdv * (centered_x - 1.0 / 255.0)
    cdf_min = approx_standard_normal_cdf(min_in)
    log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
    log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
    cdf_delta = cdf_plus - cdf_min
    log_probs = th.where(
        x < -0.999,
        log_cdf_plus,
        th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))),
    )
    assert log_probs.shape == x.shape
    return log_probs