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arXiv · 2609.14596

Direct Conditional Transition Sampling for Diffusion Inverse Problems

Qi Yu·Hanlin Wu·Xiaohui Sun
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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.

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Qi Yu, Hanlin Wu, Xiaohui Sun. 2026-09-13. Direct Conditional Transition Sampling for Diffusion Inverse Problems. https://arxiv.org/abs/2609.14596

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