Direct Conditional Transition Sampling for Diffusion Inverse Problems

Qi Yu; Hanlin Wu; Xiaohui Sun

cs.CVSep 13, 2026

Direct Conditional Transition Sampling for Diffusion Inverse Problems

Authors: Qi Yu, Hanlin Wu, Xiaohui Sun

Organizations: School of Information Science and Technology, Beijing Foreign Studies University

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.

Figures & tables

Figure 1: Comparison of three conditional transitions: (a) local guidance; (b) DAPS clean-space refresh; and (c) our proposed DCTS, which directly transports noise to the next state.

Task	Method	PSNR (dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	ArcFace $\uparrow$	Time (s) $\downarrow$
SR $\times$ 4	DAPS [ 19 ]	29.360	0.783	0.192	0.926	94.74
	DPS [ 2 ]	24.663	0.705	0.259	0.619	53.02
	MGPS [ 12 ]	28.189	0.791	0.163	0.879	81.20
	MGDM [ 7 ]	28.526	0.807	0.151	0.900	82.10
	DCTS	30.552	0.861	0.160	0.928	5.65
Phase retrieval	DAPS [ 19 ]	29.705	0.771	0.182	0.918	117.30

Table 1: Quantitative results on FFHQ-256. Best and second-best results are shown in bold and underline, respectively.

Figure 2: Visual comparison for (a) SR $\times$ 4; (b) phase retrieval; (c) deblurring; (d) colorization.

Models	PSNR(dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	ArcFace $\uparrow$
Deterministic DDIM	13.618	0.238	0.644	0.115
Stochastic DDIM ( $\eta=1$ )	16.495	0.394	0.545	0.276
Point refresh ( $M=1$ )	28.813	0.761	0.214	0.881
DCTS ( $M=8$ )	29.696	0.812	0.170	0.908

Table 2: Ablation study on the phase retrieval task.

Diffusion-Based Inverse Problems

Diffusion-based inverse problems use generative priors to recover images and physical fields from incomplete, noisy, or indirect measurements.

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Mar 9, 2026J/K move · Enter open · S save

Sparse Scheduled Diffusion Guidance for Inverse Problems

Abduragim Shtanchaev, Albina Ilina, Yazid Janati, Arip Asadulaev+2

MBZUAI, Abu Dhabi, United Arab Emirates · Institute of Foundation Models · EPITA, Paris, France

Diffusion-Based Inverse Problems Diffusion Posterior Sampling Diffusion Guidance Diffusion Timestep Scheduling

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Pretrained diffusion models are effective priors for Bayesian inverse problems, but posterior sampling with these priors is often costly because data-consistency guidance is applied throughout the full reverse trajectory. Existing methods have shown that vector-Jacobian products through the denoiser can sometimes be avoided, yet they typically still rely on dense guidance through the full trajectory or expensive inner solves. We introduce Sparse Scheduled Diffusion Guidance for Inverse Problems (Spin), a solver that avoids starting posterior sampling from pure noise. Spin first samples from a posterior time-marginal at an intermediate timestep

t_*

, and then uses that state as a warm start for a guided reverse diffusion process. At guidance time, instead of enforcing the measurement constraint at every denoising step, Spin applies lightweight corrections only at scheduled timesteps where the denoiser can still clean up artifacts. The resulting procedure decouples prior refinement from data consistency: the prior supplies denoising, while lightweight pixel-space optimization enforces the measurement constraint without backpropagation through the denoiser or decoder. Across linear and nonlinear inverse problems on FFHQ and ImageNet, Spin achieves competitive reconstruction quality with a substantially better runtime--memory profile, running 2x faster on pixel-space models and up to 50x faster on latent diffusion models, with lower memory costs.

Abstract

Diffusion-Based Inverse Problems

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