Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
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Flow Matching Guide and Code
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abstract
Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.
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representative citing papers
A control-theoretic linear program yields value-driven transport policies for generative modeling with straight paths and simulation-free training.
DiSI disentangles stochastic interpolants into separate generation and regression paths, allowing controllable transitions between regression and generative image restoration with a unified few-step sampler.
Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
FlowIQN is a quantile-coupled CFM critic that yields the first explicit Wasserstein-aligned approximate projection for distributional RL, with improved return-distribution accuracy and competitive offline RL performance.
MPFM models flow matching velocity as a Gaussian mixture prior per normal class plus a mutual information regularizer to improve open-set anomaly detection over unimodal prototypes.
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
Binomial flows close the gap between continuous flow matching and discrete ordinal data by using binomial distributions to enable unified denoising, sampling, and exact likelihoods in diffusion models.
LeapAlign fine-tunes flow matching models by constructing two consecutive leaps that skip multiple ODE steps with randomized timesteps and consistency weighting, enabling stable updates at any generation step.
TokenLight encodes lighting attributes as tokens in a conditional image generation model trained mostly on synthetic data, enabling precise relighting control and implicit learning of light-scene interactions.
DoMinO reformulates discrete flow matching sampling as an MDP for unbiased RL fine-tuning with new TV regularizers, yielding better enhancer activity and naturalness on DNA design tasks.
DiNa-LRM introduces a diffusion-native latent reward model using a noise-calibrated Thurstone likelihood on noisy states, matching VLM performance at lower compute in image alignment and preference optimization.
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
Béz ierFlow parameterizes stochastic interpolant schedulers as Béz ier functions to learn optimal sampling trajectories, achieving 2-3x better few-step performance than prior timestep optimization methods.
Reformulates constrained black-box optimization as posterior inference in latent space of flow-based models amortized by outsourced diffusion models, claiming superior performance on synthetic and real tasks.
Part²GS introduces a part-aware 3D Gaussian representation with physics-guided motion constraints and a repel point field for high-fidelity modeling of articulated objects.
DSRL steers pretrained diffusion policies for robotics by applying RL to their latent noise inputs, achieving sample-efficient real-world adaptation with only black-box access.
Analytic solution of full-batch gradient flow for linear and convolutional denoisers in diffusion models yields a universal inverse-variance spectral law for learning times of eigenmodes.
Sundial uses TimeFlow Loss for native pre-training of Transformers on continuous time series from TimeBench, achieving SOTA point and probabilistic forecasting with millisecond inference.
SITN performs single-sample OOD detection via goodness-of-fit testing on noise samples in the factorised latent space of continuous normalizing flows.
Lance presents a dual-stream mixture-of-experts model with modality-aware positional encoding and staged multi-task training that outperforms prior open-source unified models on image and video generation while keeping strong understanding performance.
Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
TOPOS creates high-fidelity 3D heads with fixed industry topology from single images via a specialized VAE with Perceiver Resampler and a rectified flow transformer.
citing papers explorer
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Quantile-Coupled Flow Matching for Distributional Reinforcement Learning
FlowIQN is a quantile-coupled CFM critic that yields the first explicit Wasserstein-aligned approximate projection for distributional RL, with improved return-distribution accuracy and competitive offline RL performance.
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Generative Modeling with Orbit-Space Particle Flow Matching
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
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Lance: Unified Multimodal Modeling by Multi-Task Synergy
Lance presents a dual-stream mixture-of-experts model with modality-aware positional encoding and staged multi-task training that outperforms prior open-source unified models on image and video generation while keeping strong understanding performance.
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TOPOS: High-Fidelity and Efficient Industry-Grade 3D Head Generation
TOPOS creates high-fidelity 3D heads with fixed industry topology from single images via a specialized VAE with Perceiver Resampler and a rectified flow transformer.
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PhyMix: Towards Physically Consistent Single-Image 3D Indoor Scene Generation with Implicit--Explicit Optimization
PhyMix unifies a new multi-aspect physics evaluator with implicit policy optimization and explicit test-time correction to produce single-image 3D indoor scenes that are both visually faithful and physically plausible.
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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.
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Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching
SharpEuler estimates a sharpness profile via finite differences on calibration trajectories, smooths it, and applies a quantile transform to generate adaptive timestep grids that improve Euler sampling quality in flow matching models at fixed budgets.
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Efficient Hierarchical Implicit Flow Q-learning for Offline Goal-conditioned Reinforcement Learning
Proposes mean flow policies and LeJEPA loss to overcome Gaussian policy limits and weak subgoal generation in hierarchical offline GCRL, reporting strong results on OGBench state and pixel tasks.
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A Survey on Vision-Language-Action Models: An Action Tokenization Perspective
The survey frames VLA models as pipelines that generate progressively grounded action tokens and classifies those tokens into eight types to guide future development.
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Intention-Conditioned Flow Occupancy Models
InFOM applies flow matching to model intention-conditioned occupancy measures for RL pre-training, reporting 1.8x median return gains and 36% higher success rates on benchmarks.
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A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
Diffusion, score-based, and flow matching models are unified as instances of learning time-dependent vector fields inducing marginal distributions governed by continuity and Fokker-Planck equations.