{"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/traversing-within-the-gaussian-typical-set","title":"Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models","arxiv_id":"2112.03860","date":"2021-12-07","proceeding":null,"authors":["Dongzhuo Li"],"abstract":"Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent tensors of such deep generative models can fall out of the desired high-dimensional standard Gaussian distribution during inversion, particularly in the presence of data noise and inaccurate forward models, leading to low-fidelity solutions. To address this issue, we propose to reparameterize and Gaussianize the latent tensors using novel differentiable data-dependent layers wherein custom operators are defined by solving optimization problems. These proposed layers constrain inverse problems to obtain high-fidelity in-distribution solutions. We validate our technique on three inversion tasks: compressive-sensing MRI, image deblurring, and eikonal tomography (a nonlinear PDE-constrained inverse problem) using two representative deep generative models: StyleGAN2 and Glow. Our approach achieves state-of-the-art performance in terms of accuracy and consistency.","url_abs":"https://arxiv.org/abs/2112.03860v5","url_pdf":"https://arxiv.org/pdf/2112.03860v5.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":"traversing-within-the-gaussian-typical-set","repo_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"},{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"eikonal-tomography","task_name":"Eikonal Tomography"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"ica","method_name":"ICA"},{"method_slug":"normalizing-flows","method_name":"Normalizing Flows"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2112.03860","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2112.03860"}},"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/lidongzh/DGM-Inv-Gaussianization","reach":null}],"summary":{"ran":4,"ran_draft_wrong":2,"ran_violates":1,"unverified":8},"by_repo_kind":{"named_in_paper":{"samples":15,"ran":7,"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":"5e99bf1ba3a7a845","entry":"_moment","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"5e99bf1ba3a7a845"}},{"code_sha256_prefix":"588962278894307c","entry":"kurtosis","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"588962278894307c"}},{"code_sha256_prefix":"72531f75392e2edf","entry":"lambertw","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"72531f75392e2edf"}},{"code_sha256_prefix":"3a7ac3ea7f27e6f4","entry":"moment","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3a7ac3ea7f27e6f4"}},{"code_sha256_prefix":"d952e4e48d093122","entry":"w_d","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d952e4e48d093122"}},{"code_sha256_prefix":"989ea922f28f905f","entry":"w_d_th","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"989ea922f28f905f"}},{"code_sha256_prefix":"2aca99248349fc3b","entry":"w_t_th","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"2aca99248349fc3b"}},{"code_sha256_prefix":"5407d531fd31dfb0","entry":"delta_gmm_custom","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"5407d531fd31dfb0"}},{"code_sha256_prefix":"fb912b0e8c67f264","entry":"delta_gmm_np","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"fb912b0e8c67f264"}},{"code_sha256_prefix":"12a51b8c827b9ece","entry":"delta_gmm_th","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"12a51b8c827b9ece"}},{"code_sha256_prefix":"63dbffe3e9047f33","entry":"delta_init","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"63dbffe3e9047f33"}},{"code_sha256_prefix":"6e589830a3b835e2","entry":"igmm","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"6e589830a3b835e2"}},{"code_sha256_prefix":"500adcb55fdf013b","entry":"inside_func_th","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"500adcb55fdf013b"}},{"code_sha256_prefix":"942c83f8430dfd6f","entry":"inside_func_th_grad","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"942c83f8430dfd6f"}},{"code_sha256_prefix":"87cce7037201ca42","entry":"lambert_transform","repo":"lidongzh/DGM-Inv-Gaussianization","repo_kind":"named_in_paper","path":"dgminv/ops/lambert_transform.py","file_url":"https://github.com/lidongzh/DGM-Inv-Gaussianization/blob/HEAD/dgminv/ops/lambert_transform.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":"87cce7037201ca42"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}