title: Consistency Flow Matching: Defining Straight Flows with Velocity
    Consistency
summary: Flow matching (FM) is a general framework for defining probability paths via
  Ordinary Differential Equations (ODEs) to transform between noise and data
  samples. Recent approaches attempt to straighten these flow trajectories to
  generate high-quality samples with fewer function evaluations, typically
  through iterative rectification methods or optimal transport solutions. In this
  paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM
  method that explicitly enforces self-consistency in the velocity field.
  Consistency-FM directly defines straight flows starting from different times to
  the same endpoint, imposing constraints on their velocity values. Additionally,
  we propose a multi-segment training approach for Consistency-FM to enhance
  expressiveness, achieving a better trade-off between sampling quality and
  speed. Preliminary experiments demonstrate that our Consistency-FM
  significantly improves training efficiency by converging 4.4x faster than
  consistency models and 1.7x faster than rectified flow models while achieving
  better generation quality. Our code is available at:
  https://github.com/YangLing0818/consistency_flow_matching
paper_authors._id: 6684acd0c1cbe5e008c99eab
paper_authors.name: Ling Yang
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-07-12T07:41:34.365Z
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paper_authors.avatarUrl: /avatars/061a69d858b86d1600be916122cae7fc.svg
paper_authors.fullname: Ling Yang
paper_authors.type: user
paper_authors.user: Lingaaaaaaa
paper_authors._id: 6684acd0c1cbe5e008c99eac
paper_authors.name: Zixiang Zhang
paper_authors._id: 6684acd0c1cbe5e008c99ead
paper_authors.name: Zhilong Zhang
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-07-03T08:20:32.301Z
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paper_authors.fullname: Zhilong Zhang
paper_authors.type: user
paper_authors.user: zzl35
paper_authors._id: 6684acd0c1cbe5e008c99eae
paper_authors.name: Xingchao Liu
paper_authors.status: admin_assigned
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paper_authors.fullname: Xingchao Liu
paper_authors.type: user
paper_authors.user: XCLiu
paper_authors._id: 6684acd0c1cbe5e008c99eaf
paper_authors.name: Minkai Xu
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-07-03T08:20:46.679Z
paper_authors._id: 64c0e950aa57599de1c75dad
paper_authors.avatarUrl: /avatars/374d53317cbccc30fae70e5152ca13e0.svg
paper_authors.fullname: Minkai Xu
paper_authors.type: user
paper_authors.user: mkxu
paper_authors._id: 6684acd0c1cbe5e008c99eb0
paper_authors.name: Wentao Zhang
paper_authors._id: 6684acd0c1cbe5e008c99eb1
paper_authors.name: Chenlin Meng
paper_authors._id: 6684acd0c1cbe5e008c99eb2
paper_authors.name: Stefano Ermon
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-07-03T08:21:23.591Z
paper_authors._id: 62f6e244329d4d014d1f4ac5
paper_authors.avatarUrl: /avatars/5a8b2bb063c2ebc340504b22530f6811.svg
paper_authors.fullname: Stefano Ermon
paper_authors.type: user
paper_authors.user: ermonste
paper_authors._id: 6684acd0c1cbe5e008c99eb3
paper_authors.name: Bin Cui
paper_title: Consistency Flow Matching: Defining Straight Flows with Velocity
    Consistency
paper_summary: Flow matching (FM) is a general framework for defining probability paths via
  Ordinary Differential Equations (ODEs) to transform between noise and data
  samples. Recent approaches attempt to straighten these flow trajectories to
  generate high-quality samples with fewer function evaluations, typically
  through iterative rectification methods or optimal transport solutions. In this
  paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM
  method that explicitly enforces self-consistency in the velocity field.
  Consistency-FM directly defines straight flows starting from different times to
  the same endpoint, imposing constraints on their velocity values. Additionally,
  we propose a multi-segment training approach for Consistency-FM to enhance
  expressiveness, achieving a better trade-off between sampling quality and
  speed. Preliminary experiments demonstrate that our Consistency-FM
  significantly improves training efficiency by converging 4.4x faster than
  consistency models and 1.7x faster than rectified flow models while achieving
  better generation quality. Our code is available at:
  https://github.com/YangLing0818/consistency_flow_matching
paper_ai_summary: Consistency Flow Matching improves the efficiency and quality of sample generation by enforcing self-consistency in velocity fields and using multi-segment training for flow-based generative models.
paper_ai_keywords: flow matching ordinary differential equations ODEs probability paths noise data samples function evaluations iterative rectification optimal transport velocity field self-consistency straight flows multi-segment training sampling quality consistency models rectified flow models