{"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/constant-acceleration-flow-1","title":"Constant Acceleration Flow","arxiv_id":"2411.00322","date":"2024-11-01","proceeding":null,"authors":["Dogyun Park","Sojin Lee","Sihyeon Kim","Taehoon Lee","Youngjoon Hong","Hyunwoo J. Kim"],"abstract":"Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at \\href{https://github.com/mlvlab/CAF}{https://github.com/mlvlab/CAF}.","url_abs":"https://arxiv.org/abs/2411.00322v1","url_pdf":"https://arxiv.org/pdf/2411.00322v1.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":"constant-acceleration-flow-1","repo_url":"https://github.com/mlvlab/CAF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-imagenet-64x64","task":"Image Generation","dataset":"ImageNet 64x64","model":"CAF","rank_in_archive_order":16,"of":65,"metrics":{"FID":"1.69","Inception Score":"62.03","NFE":"2"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2411.00322","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2411.00322"}},"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/mlvlab/CAF","reach":null}],"summary":{"ran_draft_wrong":3},"by_repo_kind":{"official":{"samples":3,"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":3,"samples":[{"code_sha256_prefix":"0e98b4fde008d871","entry":"caf_acc_defaults","repo":"mlvlab/CAF","repo_kind":"official","path":"flow/script_util.py","file_url":"https://github.com/mlvlab/CAF/blob/HEAD/flow/script_util.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"0e98b4fde008d871"}},{"code_sha256_prefix":"535c58b2b7fb357a","entry":"caf_gan_defaults","repo":"mlvlab/CAF","repo_kind":"official","path":"flow/script_util.py","file_url":"https://github.com/mlvlab/CAF/blob/HEAD/flow/script_util.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"535c58b2b7fb357a"}},{"code_sha256_prefix":"20837e056bce0de2","entry":"caf_vel_defaults","repo":"mlvlab/CAF","repo_kind":"official","path":"flow/script_util.py","file_url":"https://github.com/mlvlab/CAF/blob/HEAD/flow/script_util.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"20837e056bce0de2"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}