Direct Conditional Transition Sampling for Diffusion Inverse Problems
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× speedups over competing methods.
Related
- Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
- Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
- Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
- Inverse problems for the diffusion equation with one time observation
- Physics-Guided Conditional Flow Matching with Energy Regularization for Robust PDE Inverse Problems
BibTeX
@misc{yu2026direct,
title = {{Direct Conditional Transition Sampling for Diffusion Inverse Problems}},
author = {Qi Yu and Hanlin Wu and Xiaohui Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14596},
eprint = {2609.14596},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14596},
}
RIS
TY - UNPB
TI - Direct Conditional Transition Sampling for Diffusion Inverse Problems
AU - Qi Yu
AU - Hanlin Wu
AU - Xiaohui Sun
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14596
UR - https://arxiv.org/abs/2609.14596
AB - 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× speedups over competing methods.
ER -