Stochastic Optimal Control Sampling for Diffusion Inverse Problems

• URL: http://arxiv.org/abs/2606.28785v1
• Date: Sat, 27 Jun 2026 07:34:52 GMT
• Title: Stochastic Optimal Control Sampling for Diffusion Inverse Problems
• Abstract summary: We introduce Optimal Control Sampling (SOCS), which models the denoising process as a dynamical system and injects control signals via SOC.<n>Our method is compatible with a variety of linear differential equation reconstructions with improved visual fidelity and stronger quantitative performance.
• Score: 35.41392757423596
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Benefiting from the strong ability to capture data distributions, diffusion models have become powerful tools for solving image inverse problems. The key is to controllably steer the sampling trajectory toward the measurements while respecting the diffusion prior. In this work, we introduce Stochastic Optimal Control Sampling (SOCS), which models the denoising process as a dynamical system and injects control signals via SOC. Previous SOC-based approach addresses inverse problems by optimizing over the entire trajectory, which is computationally expensive. In contrast, we derive a closed-form control update and apply it at each sampling step, pulling the measurement-consistent clean prediction back onto the denoising flow. In SOCS, we can readily modulate the control strength to align with the diffusion model's native capabilities and thereby enhance perceptual quality. Our method is compatible with a variety of linear stochastic differential equation backbones. Extensive experiments across a broad spectrum of image inverse tasks demonstrate that SOCS achieves accurate measurement-aligned reconstructions with improved visual fidelity and stronger quantitative performance.

Related papers

• Provable diffusion-based posterior sampling for linear inverse problems via DDIM [22.029416455468063]
  We propose a simple and efficient algorithm, called pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler.<n>Our results convert posterior sampling for noisy linear inverse problems to simple coordinate-wise DDIM updates, yielding an efficient, easy-to-implement algorithm with provable posterior consistency.
  arXiv  Detail & Related papers  (2026-07-21T17:53:36Z)
• Precise: SDE-Consistent Stochastic Sampling for RL Post-Training of Flow-Matching Models [56.67321805551389]
  Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators.<n>The sampler, controlling the exploration behavior and denoising dynamics, is thus part of the policy.<n>We propose a new sampler that balances effective exploration with stability.
  arXiv  Detail & Related papers  (2026-05-22T11:37:22Z)
• Robust Posterior Diffusion-based Sampling via Adaptive Guidance Scale [39.27744518020771]
  We propose an adaptive likelihood step-size strategy to guide the diffusion process for inverse-problem formulations.<n>The resulting approach, Adaptive Posterior diffusion Sampling (AdaPS), is hyper-free and improves reconstruction quality across diverse imaging tasks.
  arXiv  Detail & Related papers  (2025-11-23T14:37:59Z)
• Coefficients-Preserving Sampling for Reinforcement Learning with Flow Matching [6.238027696245818]
  Reinforcement Learning (RL) has emerged as a powerful technique for improving image and video generation in Diffusion and Flow Matching models.<n>Our investigation reveals a significant drawback to this approach: SDE-based sampling introduces pronounced noise artifacts in the generated images.<n>Our proposed method, Coefficients-Preserving Sampling (CPS) eliminates these noise artifacts.
  arXiv  Detail & Related papers  (2025-09-07T07:25:00Z)
• Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance [52.705112811734566]
  A novel diffusion-based framework is introduced for solving inverse problems using a piecewise guidance scheme.<n>The proposed method is problem-agnostic and readily adaptable to a variety of inverse problems.<n>The framework achieves a reduction in inference time of (25%) for inpainting with both random and center masks, and (23%) and (24%) for (4times) and (8times) super-resolution tasks.
  arXiv  Detail & Related papers  (2025-07-22T19:35:14Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [70.8832906871441]
  We study how to steer generation toward desired rewards without retraining the models.<n>Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement.<n>We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Arbitrary-steps Image Super-resolution via Diffusion Inversion [68.78628844966019]
  This study presents a new image super-resolution (SR) technique based on diffusion inversion, aiming at harnessing the rich image priors encapsulated in large pre-trained diffusion models to improve SR performance.<n>We design a Partial noise Prediction strategy to construct an intermediate state of the diffusion model, which serves as the starting sampling point.<n>Once trained, this noise predictor can be used to initialize the sampling process partially along the diffusion trajectory, generating the desirable high-resolution result.
  arXiv  Detail & Related papers  (2024-12-12T07:24:13Z)
• Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems [12.482127049881026]
  We propose a novel approach to solve inverse problems with a diffusion prior from an amortized variational inference perspective. Our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements.
  arXiv  Detail & Related papers  (2024-07-23T02:14:18Z)
• Deep Equilibrium Diffusion Restoration with Parallel Sampling [120.15039525209106]
  Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Most existing methods need long serial sampling chains to restore HQ images step-by-step, resulting in expensive sampling time and high computation costs. In this work, we aim to rethink the diffusion model-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system, called DeqIR.
  arXiv  Detail & Related papers  (2023-11-20T08:27:56Z)
• A Variational Perspective on Solving Inverse Problems with Diffusion Models [101.831766524264]
  Inverse tasks can be formulated as inferring a posterior distribution over data. This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. We propose a variational approach that by design seeks to approximate the true posterior distribution.
  arXiv  Detail & Related papers  (2023-05-07T23:00:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.