{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/solving-inverse-problems-via-diffusion","title":"Solving Inverse Problems via Diffusion Optimal Control","arxiv_id":"2412.16748","date":"2024-12-21","proceeding":null,"authors":["Henry Li","Marcus Pereira"],"abstract":"Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several critical drawbacks, including the intractability of the conditional likelihood function, strict dependence on the score network approximation, and poor $\\mathbf{x}_0$ prediction quality. We demonstrate that these limitations can be sidestepped by reframing the generative process as a discrete optimal control episode. We derive a diffusion-based optimal controller inspired by the iterative Linear Quadratic Regulator (iLQR) algorithm. This framework is fully general and able to handle any differentiable forward measurement operator, including super-resolution, inpainting, Gaussian deblurring, nonlinear deblurring, and even highly nonlinear neural classifiers. Furthermore, we show that the idealized posterior sampling equation can be recovered as a special case of our algorithm. We then evaluate our method against a selection of neural inverse problem solvers, and establish a new baseline in image reconstruction with inverse problems.","url_abs":"https://arxiv.org/abs/2412.16748v1","url_pdf":"https://arxiv.org/pdf/2412.16748v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"solving-inverse-problems-via-diffusion","repo_url":"https://github.com/lihenryhfl/diffusion_optimal_control","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2412.16748","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2412.16748"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lihenryhfl/diffusion_optimal_control","reach":null}],"summary":{"ran":2,"ran_draft_wrong":1,"unverified":2},"by_repo_kind":{"official":{"samples":5,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"1c5e1bfb04b70e0c","entry":"DDP","repo":"lihenryhfl/diffusion_optimal_control","repo_kind":"official","path":"optimizers/mfddp.py","file_url":"https://github.com/lihenryhfl/diffusion_optimal_control/blob/HEAD/optimizers/mfddp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1c5e1bfb04b70e0c"}},{"code_sha256_prefix":"3fa10fb6aafd5454","entry":"MFDDP","repo":"lihenryhfl/diffusion_optimal_control","repo_kind":"official","path":"optimizers/mfddp.py","file_url":"https://github.com/lihenryhfl/diffusion_optimal_control/blob/HEAD/optimizers/mfddp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3fa10fb6aafd5454"}},{"code_sha256_prefix":"fd57d8e6b5de11d3","entry":"register_sampler","repo":"lihenryhfl/diffusion_optimal_control","repo_kind":"official","path":"utils/gaussian_diffusion.py","file_url":"https://github.com/lihenryhfl/diffusion_optimal_control/blob/HEAD/utils/gaussian_diffusion.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fd57d8e6b5de11d3"}},{"code_sha256_prefix":"294fde7d083cb8c9","entry":"create_sampler","repo":"lihenryhfl/diffusion_optimal_control","repo_kind":"official","path":"utils/gaussian_diffusion.py","file_url":"https://github.com/lihenryhfl/diffusion_optimal_control/blob/HEAD/utils/gaussian_diffusion.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"294fde7d083cb8c9"}},{"code_sha256_prefix":"3c731f22d73494cc","entry":"get_sampler","repo":"lihenryhfl/diffusion_optimal_control","repo_kind":"official","path":"utils/gaussian_diffusion.py","file_url":"https://github.com/lihenryhfl/diffusion_optimal_control/blob/HEAD/utils/gaussian_diffusion.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3c731f22d73494cc"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}