# Direct Conditional Transition Sampling for Diffusion Inverse Problems

arXiv: https://arxiv.org/abs/2609.14596 · HTML: https://mlsanity.com/paper/2609.14596/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [A Mixture-Based Framework for Guiding Diffusion Models](https://mlsanity.com/paper/2502.03332/) (2025)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling](https://mlsanity.com/paper/2409.08906/) (2024)

## Abstract (arXiv)

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.