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| # 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 torch as th | |
| import numpy as np | |
| 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. | |
| """ | |
| # scalars - 标量. 广播机制允许NumPy在执行算术运算时处理不同形状（shape）的数组，相当于自动扩展 reshape | |
| 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).to(tensor) | |
| for x in (logvar1, logvar2) | |
| ] | |
| return 0.5 * ( | |
| -1.0 | |
| + logvar2 | |
| - logvar1 | |
| + th.exp(logvar1 - logvar2) | |
| + ((mean1 - mean2) ** 2) * th.exp(-logvar2) | |
| ) | |
| ''' | |
| cdf - cumulative distribution function, 累计分布函数, 是概率密度函数的积分 | |
| cdf 用来刻画分布概率, 在 nerf 中找出 density 大, 光线被吸收较多的区域 | |
| 用于渲染时, 通过 cdf 来计算光线被吸收的概率 | |
| ''' | |
| 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)))) | |
| ''' | |
| 计算高斯似然 | |
| 似然用于做参数估计, 即在观测到一些数据样本的情况下, 通过最大似然估计的方法, 估计出最有可能的参数值 θ = argmax P(X|θ) | |
| ''' | |
| 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 | |
| ''' | |
| 离散化的高斯函数似然估计 | |
| ''' | |
| 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 | |