Direct Conditional Transition Sampling for Diffusion Inverse Problems

2026-09-13

AI Summary

本文提出直接条件转换采样法解决扩散逆问题，通过估计测量条件下的清洁均值并直接将高斯源噪声传输到下一个噪声状态，实现快速准确的重建。

Abstract

Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent posterior refresh can improve global correction by sampling a clean conditional and re-noising it, but its practical realization requires probability-flow ODE integration and clean-space Markov chain Monte Carlo (MCMC). We propose Direct Conditional Transition Sampling (DCTS), a direct stochastic-flow approximation to the same ideal refresh target. Rather than explicitly drawing a clean sample, DCTS estimates the measurement-conditioned clean mean along a short inner path and transports Gaussian source noise directly to the next noisy state. A denoiser-compatible sufficient statistic and a covariance-scaled operator update enable this conditional-mean estimation. Experiments on four inverse problems demonstrate that DCTS achieves competitive reconstruction quality with up to $16.8\times$ speedups over competing methods.

Problem

• diffusion inverse problems
• posterior updates
• probability-flow ODE

Innovation

• Direct Conditional Transition Sampling
• diffusion inverse problems
• Gaussian source noise
• denoiser-compatible sufficient statistic
• covariance-scaled operator update