REVIEW 33 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
Flow map matching with stochastic interpolants: A mathematical framework for consistency models
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.
Forward citations
Cited by 33 Pith papers
-
Strong Stochastic Flow Maps
Strong Stochastic Flow Maps learn the strong solution map of additive-noise SDEs via a pathwise-convergent polynomial Brownian approximation, generalizing deterministic flow maps and enabling simulation-free training ...
-
AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation
AnyFlow enables any-step video diffusion by distilling flow-map transitions over arbitrary time intervals with on-policy backward simulation.
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at tex...
-
Flow Reasoning Models: Scaling Reasoning Through Iterative Self-Refinement
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
-
Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metrics
Naive samplers beat published diffusion and flow models on gen-PPL with incoherent output, proving the metric unsound and motivating distributional evaluation suites.
-
DriftXpress: Faster Drifting Models via Projected RKHS Fields
DriftXpress approximates drifting kernels via projected RKHS fields to lower training cost of one-step generative models while matching original FID scores.
-
Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models
Reinforce Adjoint Matching derives a simple consistency loss for RL post-training of diffusion models by tilting the clean distribution toward higher-reward samples under KL regularization while keeping the noising pr...
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG is a training-free, single-trajectory guidance method for flow models derived from optimal control that achieves strong reward alignment with only 3 NFEs.
-
Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
Isokinetic Flow Matching adds a lightweight regularization term to flow matching that penalizes acceleration along paths via self-guided finite differences, yielding straighter trajectories and large gains in few-step...
-
Flow Map Language Models: One-step Language Modeling via Continuous Denoising
Continuous flow language models match discrete diffusion baselines and their distilled one-step flow map versions exceed 8-step discrete diffusion quality on LM1B and OWT.
-
One Step Diffusion via Shortcut Models
Shortcut models enable high-quality single or few-step sampling in diffusion models with one network and training phase by conditioning on desired step size.
-
Amortized Moment Matching for Visual Generation
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.
-
Flow Map Learning via Nongradient Vector Flow
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.
-
Parallel Decoding Distillation for Fast Image and Video Generation
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.
-
Diffusion Fine-tuning with Rewarded Moment Matching Distillation
RMMD simultaneously distills diffusion models and optimizes rewards, yielding better FID-reward trade-offs on ImageNet than DI++, DRaFT and HyperNoise, and a 7.5x faster GenCast model that beats its teacher on 93% of ...
-
Posterior Refinement: Fast Language Generation via Any-Order Flow Maps
FMLM+ with Posterior Refinement bridges masked diffusion and flow map models to match discrete baseline quality in language generation using 32x fewer neural function evaluations via posterior scoring and refinement.
-
Fast and Highly Expressive Policy Learning for Offline Reinforcement Learning via Bootstrapped Flow Q-Learning
BFQ enables single-step noise-to-action mapping in offline RL by dividing flow-path displacements into bootstrappable short-range components learned from marginal velocity.
-
Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models
Derives RAM, a reward-adjusted consistency loss extending diffusion pretraining regression to efficient KL-regularized RL post-training, achieving peak rewards up to 50x faster than Flow-GRPO on Stable Diffusion 3.5M.
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG is a training-free single-trajectory guidance framework for flow-based models that matches or exceeds baselines on reward-guided tasks and inverse problems using as few as 3 NFEs.
-
Extending One-Step Image Generation from Class Labels to Text via Discriminative Text Representation
By requiring and using highly discriminative LLM text features, the work enables the first effective one-step text-conditioned image generation with MeanFlow.
-
Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery
A framework learns fault-indexed Perron-Frobenius operators from trajectory data to provide certifiable 2-Wasserstein bounds for detecting actuator faults and enabling recovery via density propagation in nonlinear con...
-
ODE-free Neural Flow Matching for One-Step Generative Modeling
OT-NFM parameterizes the flow map directly with neural flows and uses optimal transport for consistent noise-data couplings to achieve ODE-free one-step generation while avoiding mean collapse.
-
Salt: Self-Consistent Distribution Matching with Cache-Aware Training for Fast Video Generation
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.
-
Salt: Self-Consistent Distribution Matching with Cache-Aware Training for Fast Video Generation
Salt improves low-step video generation quality by adding endpoint-consistent regularization to distribution matching distillation and using cache-conditioned feature alignment for autoregressive models.
-
A Unified View of Score-Based and Drifting Models
Drifting with Gaussian kernels exactly matches score-matching on smoothed distributions via Tweedie's formula, while Laplace kernels approximate this closely in high dimensions.
-
Flow Map Language Models: One-step Language Modeling via Continuous Denoising
Continuous flows on token embeddings with flow-map distillation produce one-step language models whose quality exceeds recent 8-step discrete diffusion baselines on LM1B and OpenWebText.
-
Dual-End Consistency Model
DE-CM reaches state-of-the-art one-step FID of 1.70 on ImageNet 256x256 by decomposing PF-ODE trajectories into three critical sub-trajectories and using flow matching plus N2N mapping for stability.
-
Mean Flows for One-step Generative Modeling
MeanFlow uses a derived identity between average and instantaneous velocities to train one-step flow models, achieving FID 3.43 on ImageNet 256x256 with 1-NFE from scratch.
-
FlowCTS: On-policy Continuous Trajectory Supervision of Flow Models
Trajectory-derived, temporally weighted velocity matching from shared student states outperforms KL-based on-policy distillation for multi-reference flow model post-training.
-
Layer-Parallel Inference Reduces Encrypted Nonlinear Depth in Transformers
SNLP reduces encrypted Transformer nonlinear depth from L sequential stages to (L−N)+K, cutting symbolic bootstraps ~2.65× with lower error amplification than sequential inference.
-
Layer-Parallel Inference Reduces Encrypted Nonlinear Depth in Transformers
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.
-
Measure-to-measure Regression with Transformers
Formalizes nonlinear M2M regression and introduces transformer architectures as static maps and dynamic velocity fields between probability measures, tested on synthetic, particle, and organoid datasets.
-
The Principles of Diffusion Models
A monograph that unifies variational, score-based, and flow-based views of diffusion models around a common time-dependent velocity field whose flow is solved as a differential equation to generate data from noise.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.