We define a broader family of corruption processes that generalizes
previously known diffusion models. To reverse these general diffusions, we
propose a new objective called Soft Score Matching that provably learns the
score function for any linear corruption process and yields state of the art
results for CelebA. Soft Score Matching incorporates the degradation process in
the network. Our new loss trains the model to predict a clean image,
\textit{that after corruption}, matches the diffused observation. We show that
our objective learns the gradient of the likelihood under suitable regularity
conditions for a family of corruption processes. We further develop a
principled way to select the corruption levels for general diffusion processes
and a novel sampling method that we call Momentum Sampler. We show
experimentally that our framework works for general linear corruption
processes, such as Gaussian blur and masking. We achieve state-of-the-art FID
score $1.85$ on CelebA-64, outperforming all previous linear diffusion models.
We also show significant computational benefits compared to vanilla denoising
diffusion.

定义并推广了一类更广泛的腐败过程，引入 Soft Score Matching 目标函数并证明其可学习任何线性腐败过程的得分函数，从而实现了对一般扩散过程的逆反操作并取得了最新的实验结果。

软扩散：通用扰动的得分匹配

Soft Diffusion: Score Matching for General Corruptions

Denoising diffusion probabilistic models (DDPMs) have shown impressive
results on sequence generation by iteratively corrupting each example and then
learning to map corrupted versions back to the original. However, previous work
has largely focused on in-place corruption, adding noise to each pixel or token
individually while keeping their locations the same. In this work, we consider
a broader class of corruption processes and denoising models over sequence data
that can insert and delete elements, while still being efficient to train and
sample from. We demonstrate that these models outperform standard in-place
models on an arithmetic sequence task, and that when trained on the text8
dataset they can be used to fix spelling errors without any fine-tuning.

本文提出了一种更广泛的 DDPMs，能够处理序列数据中插入和删除元素的噪声，该模型在算术序列任务和 text8 数据集上表现出较好的结果，并可用于拼写错误的修复。