{"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/estimating-high-order-gradients-of-the-data","title":"Estimating High Order Gradients of the Data Distribution by Denoising","arxiv_id":"2111.04726","date":"2021-11-08","proceeding":"NeurIPS 2021 12","authors":["Chenlin Meng","Yang song","Wenzhe Li","Stefano Ermon"],"abstract":"The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.","url_abs":"https://arxiv.org/abs/2111.04726v1","url_pdf":"https://arxiv.org/pdf/2111.04726v1.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":[],"tasks":[{"task_slug":"audio-synthesis","task_name":"Audio Synthesis"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[{"method_slug":"denoising-score-matching","method_name":"Denoising Score Matching"},{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2111.04726","atlas_url":"https://app.syntology.ai/?focus=2111.04726","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2111.04726"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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":"deterministic:regex_extraction","url":"https://github.com/ermongroup/ncsn","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"found_in_text":{"samples":1,"ran":1,"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":1,"samples":[{"code_sha256_prefix":"1492fccd0aa41223","entry":"dsm","repo":"ermongroup/ncsn","repo_kind":"found_in_text","path":"losses/dsm.py","file_url":"https://github.com/ermongroup/ncsn/blob/HEAD/losses/dsm.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"1492fccd0aa41223"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}