Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems

[2608.14744] Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14744 (cs) [Submitted on 13 Aug 2026] Title: Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems Authors: Mrigank Dhingra , Ramchandran Muthukumar , Rebecca Willett , Omer San View a PDF of the paper titled Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems, by Mrigank Dhingra and 3 other authors View PDF HTML (experimental) Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation exploits temporal information through forecast-analysis cycles, but often requires repeated access to expensive high-resolution forecast models. Generative super-resolution can recover unresolved structure from coarse observations, but is commonly used as a one-shot mapping that does not fully exploit constraints from past states. We introduce Iterative Refinement (IR), a learned data assimilation framework that combines these perspectives. Instead of performing a single coarse-to-fine reconstruction, IR decomposes the task into resolution-wise forecast-analysis operations across a multiresolution hierarchy. At each stage, a shared neural operator with resolution-dependent spectral mode slicing provides a dynamical prior, while a shared conditional diffusion corrector uses the current coarser-resolution state to produce a refined posterior at the next finer resolution. We evaluate IR on one-dimensional stochastically forced Burgers dynamics and two-dimensional Kraichnan turbulence. On the challenging 256x256 Kraichnan benchmark, IR achieves an RMSE of 0.184 and an SSIM of 0.836, outperforming spectral upsampling, one-shot diffusion super-resolution, enhanced deep super-resolution, and an autoregressive forecaster. On the more constrained Burgers testbed, IR remains competitive with one-shot diffusion, which achieves the lowest RMSE. These results show that one-shot generative reconstruction can be effective for simpler settings, while hierarchical forecast-analysis refinement becomes advantageous in strongly multiscale and underdetermined regimes. Overall, IR combines temporal priors, generative correction, and multiresolution reconstruction for learned data assimilation in complex physical systems. Subjects: Machine Learning (cs.LG) ; Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2608.14744 [cs.LG] (or arXiv:2608.14744v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14744 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mrigank Dhingra [ view email ] [v1] Thu, 13 Aug 2026 22:45:40 UTC (27,339 KB) Full-text links: Access Paper: View a PDF of the paper titled Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems, by Mrigank Dhingra and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs physics physics.flu-dyn References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Tempered Guided Diffusion#155309
• Mixed finite element methods for a class of nonlinear reaction diffusion problems#395165
• Physical Fidelity of Wave-Based Inverse Problems under Broken Time-Reversal Symmetry#1064810
• Coherent Phonon Blocking in Superlattices#609299
• Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations#324889