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[2602.21469] D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching
Summary
The paper presents D-Flow SGLD, a method for source-space posterior sampling in scientific inverse problems, enhancing fidelity and uncertainty quantification without retraining models.
Why It Matters
This research addresses the challenge of reconstructing high-dimensional physical states from limited data, which is crucial in fields like meteorology and engineering. By improving posterior sampling methods, it enhances predictive accuracy and reliability in scientific applications.
Key Takeaways
- D-Flow SGLD enables scalable exploration of source posteriors without retraining models.
- The method integrates likelihood information for improved measurement assimilation.
- It benchmarks against existing methods across various scientific problems, demonstrating superior fidelity.
- The approach maintains physics/statistics fidelity while enhancing posterior diversity.
- D-Flow SGLD is positioned as a practical solution for scientific inverse problems.
Computer Science > Machine Learning arXiv:2602.21469 (cs) [Submitted on 25 Feb 2026] Title:D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching Authors:Meet Hemant Parikh, Yaqin Chen, Jian-Xun Wang View a PDF of the paper titled D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching, by Meet Hemant Parikh and 2 other authors View PDF HTML (experimental) Abstract:Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and governing physics. While training-free conditional generation is well developed for diffusion models, corresponding conditioning and posterior sampling strategies for Flow Matching (FM) priors remain comparatively under-explored, especially on scientific benchmarks where fidelity must be assessed beyond measurement misfit. In this work, we study training-free conditional generation for scientific inverse problems under FM priors and organize existing inference-time strategies by where measurement information is injected: (i) guided transport dynamics that perturb sampling trajectories using likelihood information, and (ii) source-distribution inference that performs posterior inference over the source variable while keeping the learned transport fixed. Building on the latter, we propose D-Flow SGLD, a s...
