Denoising diffusion models (DDM) have gained recent traction in medical image
translation given improved training stability over adversarial models. DDMs
learn a multi-step denoising transformation to progressively map random
Gaussian-noise images onto target-modality images, while receiving stationary
guidance from source-modality images. As this denoising transformation diverges
significantly from the task-relevant source-to-target transformation, DDMs can
suffer from weak source-modality guidance. Here, we propose a novel
self-consistent recursive diffusion bridge (SelfRDB) for improved performance
in medical image translation. Unlike DDMs, SelfRDB employs a novel forward
process with start- and end-points defined based on target and source images,
respectively. Intermediate image samples across the process are expressed via a
normal distribution with mean taken as a convex combination of start-end
points, and variance from additive noise. Unlike regular diffusion bridges that
prescribe zero variance at start-end points and high variance at mid-point of
the process, we propose a novel noise scheduling with monotonically increasing
variance towards the end-point in order to boost generalization performance and
facilitate information transfer between the two modalities. To further enhance
sampling accuracy in each reverse step, we propose a novel sampling procedure
where the network recursively generates a transient-estimate of the target
image until convergence onto a self-consistent solution. Comprehensive analyses
in multi-contrast MRI and MRI-CT translation indicate that SelfRDB offers
superior performance against competing methods.

医学图像翻译中，自洽递归扩散桥 (SelfRDB) 通过使用以目标图像为基础、源图像为参照的前向过程，以及噪声调度和采样过程等创新方法，提供了优越的性能。

医学图像翻译的自一致递归扩散桥

Self-Consistent Recursive Diffusion Bridge for Medical Image Translation

Denoising diffusion probabilistic models (DDPMs) are a class of powerful
generative models. The past few years have witnessed the great success of DDPMs
in generating high-fidelity samples. A significant limitation of the DDPMs is
the slow sampling procedure. DDPMs generally need hundreds or thousands of
sequential function evaluations (steps) of neural networks to generate a
sample. This paper aims to develop a fast sampling method for DDPMs requiring
much fewer steps while retaining high sample quality. The inference process of
DDPMs approximates solving the corresponding diffusion ordinary differential
equations (diffusion ODEs) in the continuous limit. This work analyzes how the
backward error affects the diffusion ODEs and the sample quality in DDPMs. We
propose fast sampling through the \textbf{Restricting Backward Error schedule
(RBE schedule)} based on dynamically moderating the long-time backward error.
Our method accelerates DDPMs without any further training. Our experiments show
that sampling with an RBE schedule generates high-quality samples within only 8
to 20 function evaluations on various benchmark datasets. We achieved 12.01 FID
in 8 function evaluations on the ImageNet $128\times128$, and a $20\times$
speedup compared with previous baseline samplers.

本研究提出了一种基于 “限制后向误差进度表”（RBE 进度表）的快速采样方法，使 Denoising Diffusion Probabilistic Models（DDPM）拥有更快的采样速度而不需要进一步训练，并在各种基准数据集上实现了高品质图像的生成。

透过误差分析的角度快速扩散概率模型采样

Fast Diffusion Probabilistic Model Sampling through the lens of Backward  Error Analysis

The past few years have witnessed the great success of Diffusion models~(DMs)
in generating high-fidelity samples in generative modeling tasks. A major
limitation of the DM is its notoriously slow sampling procedure which normally
requires hundreds to thousands of time discretization steps of the learned
diffusion process to reach the desired accuracy. Our goal is to develop a fast
sampling method for DMs with a much less number of steps while retaining high
sample quality. To this end, we systematically analyze the sampling procedure
in DMs and identify key factors that affect the sample quality, among which the
method of discretization is most crucial. By carefully examining the learned
diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS).
It is based on the Exponential Integrator designed for discretizing ordinary
differential equations (ODEs) and leverages a semilinear structure of the
learned diffusion process to reduce the discretization error. The proposed
method can be applied to any DMs and can generate high-fidelity samples in as
few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU
to generate $50k$ images from CIFAR10. Moreover, by directly using pre-trained
DMs, we achieve the state-of-art sampling performance when the number of score
function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID,
and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at
this https URL

研究 Diffusion models（DMs）的采样过程，提出了一种基于指数积分器的采样方法，可以在较少的步骤中生成高保真的样本，并在有限的评分功能评估数下达到最新的采样性能。