Pith. sign in

REVIEW 16 cited by

Flow map matching with stochastic interpolants: A mathematical framework for consistency models

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2406.07507 v2 pith:CLNFID3B submitted 2024-06-11 cs.LG math.DS

classification cs.LGmath.DS
keywords flowmodelsconsistencyframeworkmatchingdistillationdynamicalgeneration
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled efficient one-step or few-step generation, yet despite their practical success, a systematic understanding of their design has been hindered by the lack of a comprehensive theoretical framework. Here we introduce Flow Map Matching (FMM), a principled framework for learning the two-time flow map of an underlying dynamical generative model, thereby providing this missing mathematical foundation. Leveraging stochastic interpolants, we propose training objectives both for distillation from a pre-trained velocity field and for direct training of a flow map over an interpolant or a forward diffusion process. Theoretically, we show that FMM unifies and extends a broad class of existing approaches for fast sampling, including consistency models, consistency trajectory models, and progressive distillation. Experiments on CIFAR-10 and ImageNet-32 highlight that our approach can achieve sample quality comparable to flow matching while reducing generation time by a factor of 10-20.

Discussion (0). Sign in to comment.

Forward citations

Cited by 16 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Beckmann Transport Models: From Autonomous Flows to One-Step Maps

    cs.LG 2026-08 reject novelty 8.0 of 10

    An autonomous (time-independent) flow-matching drift that obeys a simple divergence equation exactly transports samples to singular targets, yielding a corrected Equilibrium Matching loss and a one-step map.

  2. Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metrics

    cs.CL 2026-06 conditional novelty 7.0 of 10

    Zero-parameter naive samplers achieve state-of-the-art generative perplexity while producing incoherent text, proving the metric is unsound; distributional divergences like MAUVE and energy distance correctly rank the...

  3. DriftXpress: Faster Drifting Models via Projected RKHS Fields

    cs.LG 2026-05 unverdicted novelty 7.0 of 10

    DriftXpress approximates the attraction field of drifting models with a Nyström landmark projection, reducing training time by 2.6–6.7× at comparable FID.

  4. Amortized Moment Matching for Visual Generation

    cs.LG 2026-07 accept novelty 6.0 of 10

    Amortized Fréchet Distance uses neural nets to match conditional means and covariances, yielding stronger one-step visual generators than explicit FD-loss or multi-step teachers.

  5. Flow Map Learning via Nongradient Vector Flow

    cs.LG 2026-07 conditional novelty 6.0 of 10

    SGFlow learns the integral map of a probability-flow ODE via a stop-gradient loss whose only stationary point is the true flow map, and it reaches the best-in-comparison FID at 10 steps on CIFAR-10.

  6. Parallel Decoding Distillation for Fast Image and Video Generation

    cs.CV 2026-07 conditional novelty 6.0 of 10

    A trajectory-based distillation method trains a student to predict multiple mean velocities per network evaluation, enabling 4-8 step generation with competitive quality and improved diversity.

  7. Salt: Self-Consistent Distribution Matching with Cache-Aware Training for Fast Video Generation

    cs.CV 2026-04 unverdicted novelty 6.0 of 10

    Self-consistent distribution matching plus cache-aware mixed-step training improves 2–4 NFE video quality on Wan 2.1 and real-time autoregressive backbones without extra inference cost.

  8. Dual-End Consistency Model

    cs.CV 2026-02 unverdicted novelty 6.0 of 10

    DE-CM trains a flow-map consistency model on three sub-trajectories (coupling, instantaneous, noise-to-noisy) and reports 1.70 FID one-step on ImageNet 256.

  9. Transition Matching Distillation for Fast Video Generation

    cs.CV 2026-01 conditional novelty 6.0 of 10

    Splitting a video diffusion model into a fixed feature extractor and a small recurrent flow head lets TMD generate videos in one to two effective steps with better VBench scores than prior distilled models.

  10. DASIP: Dynamic Test-Time Compute Scaling for Robot Control with Stochastic Interpolant Policies

    cs.RO 2025-11 reject novelty 6.0 of 10

    A difficulty classifier adaptively selects step count, solver, and ODE/SDE mode for stochastic-interpolant robot policies, reporting 2.6–4.4x compute savings with roughly unchanged success rates.

  11. Understanding, Accelerating, and Improving MeanFlow Training

    cs.CV 2025-11 conditional novelty 6.0 of 10

    Training MeanFlow by first forming instantaneous velocity and short-gap average velocity, then shifting to long gaps, improves 1-NFE ImageNet FID from 3.43 to 2.87 and speeds training by about 2.5x.

  12. Populate-A-Scene: Affordance-Aware Human Video Generation

    cs.CV 2025-07 conditional novelty 6.0 of 10

    A fine-tuned text-to-video model inserts a person into a scene and generates an interaction video without bounding boxes or pose input, and its attention maps reveal a latent sense of affordance.

  13. FlowCTS: On-policy Continuous Trajectory Supervision of Flow Models

    cs.LG 2026-07 conditional novelty 5.5 of 10

    Trajectory-derived, temporally weighted velocity matching from shared student states outperforms KL-based on-policy distillation for multi-reference flow model post-training.

  14. Layer-Parallel Inference Reduces Encrypted Nonlinear Depth in Transformers

    cs.LG 2026-07 conditional novelty 5.5 of 10

    SNLP reduces symbolic FHE bootstraps from 53 to 20 on a 0.5B model with +1.2% PPL degradation and lower polynomial-error amplification than sequential inference.

  15. Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach

    cs.LG 2025-06 conditional novelty 5.0 of 10

    A weighted-particle sampler evolves the posterior through the diffusion model's reverse dynamics, with theoretical error bounds and improved image reconstructions.

  16. The Principles of Diffusion Models

    cs.LG 2025-10 unverdicted novelty 3.0 of 10

    A principled monograph showing that variational, score-based, and flow-based diffusion models are instances of one continuous-time transport backbone, with sampling equal to solving a differential equation governed by...

Pith tools