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.
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