Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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Density estimation using Real NVP
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abstract
Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.
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representative citing papers
Rectified flow learns straight-path neural ODEs for distribution transport, yielding efficient generative models and domain transfers that work well even with a single simulation step.
Introduces an SDE-based framework for score-based generative modeling that unifies prior methods, enables predictor-corrector sampling and neural ODE likelihoods, and achieves SOTA unconditional image generation on CIFAR-10.
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
Denoising diffusion probabilistic models generate high-quality images by learning to reverse a fixed forward diffusion process, achieving FID 3.17 on CIFAR10.
A flow matching generative model produces weak lensing mass maps with fidelity improved to below 1% and 5% on basic and higher-order statistics relative to GAN benchmarks.
DriftXpress approximates drifting kernels via projected RKHS fields to lower training cost of one-step generative models while matching original FID scores.
NTM models each generative reverse step as a conditional normalizing flow with a hybrid shallow-deep architecture, enabling exact-likelihood training and strong four-step sampling performance on text-to-image tasks.
Neural scaling laws are invariant under bijective data transformations and change predictably with information resolution ρ under non-bijective transformations, enabling cross-domain transport of fitted exponents.
TRACE creates valid conformal prediction sets for complex generative models by scoring outputs via averaged denoising or velocity errors along stochastic transport paths instead of likelihoods.
A nonparametric pixel-based Bayesian method integrates TMD evolution with generative AI sampling and SVD to extract parton distributions and identify unconstrained null components from multi-scale observables.
Risk-controlled post-processing yields a threshold-structured policy that follows the baseline except where an oracle fallback sharply reduces conditional violation risk, achieving O(log n/n) expected excess risk in i.i.d. settings and exact risk control under exchangeability.
NF-NPCDR enhances neural processes with normalizing flows to model personalized multi-interest preferences and uses a preference pool plus adaptive decoder to improve cross-domain recommendations for cold-start users.
MOFAT applied to SN2024ggi shows CO triggering inner SiO formation with a receding edge, order-of-magnitude mass drop, clumping signatures, and no dust formation.
MorphoFlow learns compact probabilistic 3D shape representations from sparse annotations using neural implicits, autodecoders, autoregressive flows, and adaptive sparsity priors on latent dimensions.
VaFES constructs a latent space from reversible collective variables and variationally optimizes a tractable-density generative model to produce a continuous free energy surface from which rare events are directly sampled.
Differentiable nonconformity scores induce flows that sample conformal prediction set boundaries, and mixing flows across levels produces conformal predictive distributions whose quantiles match the sets.
ARDIS enables arbitrary-resolution deep image steganography via frequency decoupling in hiding and latent-guided implicit reconstruction for blind recovery.
RGFlow uses flow-based neural networks to learn bijective real-space RG transformations for the 2D phi^4 theory, identifying a Wilson-Fisher-like critical point and estimating the correlation length exponent.
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.
vsOED uses a variational one-point reward and RL policy optimization to provide a lower bound on expected information gain for sequential experimental design, supporting nuisance parameters, implicit likelihoods, and multiple design goals.
Proposes cINN architecture for conditional image generation that by construction yields diverse sharp samples, demonstrated on MNIST digit generation and image colorization with latent space manipulation.
TrajVAD shows that bounding-box trajectories modeled via normalizing flows can serve as a primary cue for video anomaly detection, with the trajectory-only variant achieving 87.7% AP on ShanghaiTech and best results on MSAD.
UST-Hand is a self-supervised 3D hand pose estimation method using conditional normalizing flows for uncertainty-aware hypothesis sampling and probabilistic point cloud interactions to achieve up to 37.8% better MPVPE than prior self-supervised approaches on three datasets.
citing papers explorer
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Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
Rectified flow learns straight-path neural ODEs for distribution transport, yielding efficient generative models and domain transfers that work well even with a single simulation step.
-
Score-Based Generative Modeling through Stochastic Differential Equations
Introduces an SDE-based framework for score-based generative modeling that unifies prior methods, enables predictor-corrector sampling and neural ODE likelihoods, and achieves SOTA unconditional image generation on CIFAR-10.
-
Denoising Diffusion Implicit Models
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
-
Denoising Diffusion Probabilistic Models
Denoising diffusion probabilistic models generate high-quality images by learning to reverse a fixed forward diffusion process, achieving FID 3.17 on CIFAR10.
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Increasing the Precision of Surrogate Models for Weak Lensing Mass Maps with Flow Matching
A flow matching generative model produces weak lensing mass maps with fidelity improved to below 1% and 5% on basic and higher-order statistics relative to GAN benchmarks.
-
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.
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Normalizing Trajectory Models
NTM models each generative reverse step as a conditional normalizing flow with a hybrid shallow-deep architecture, enabling exact-likelihood training and strong four-step sampling performance on text-to-image tasks.
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On the Invariance and Generality of Neural Scaling Laws
Neural scaling laws are invariant under bijective data transformations and change predictably with information resolution ρ under non-bijective transformations, enabling cross-domain transport of fitted exponents.
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TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models
TRACE creates valid conformal prediction sets for complex generative models by scoring outputs via averaged denoising or velocity errors along stochastic transport paths instead of likelihoods.
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TMDs in the Lens of Generative AI: A Pixel-Based Approach to Partonic Imaging
A nonparametric pixel-based Bayesian method integrates TMD evolution with generative AI sampling and SVD to extract parton distributions and identify unconstrained null components from multi-scale observables.
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Risk-Controlled Post-Processing of Decision Policies
Risk-controlled post-processing yields a threshold-structured policy that follows the baseline except where an oracle fallback sharply reduces conditional violation risk, achieving O(log n/n) expected excess risk in i.i.d. settings and exact risk control under exchangeability.
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Personalized Multi-Interest Modeling for Cross-Domain Recommendation to Cold-Start Users
NF-NPCDR enhances neural processes with normalizing flows to model personalized multi-interest preferences and uses a preference pool plus adaptive decoder to improve cross-domain recommendations for cold-start users.
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Probing the 3D Structures of Supernovae through IR Signatures of CO and SiO
MOFAT applied to SN2024ggi shows CO triggering inner SiO formation with a receding edge, order-of-magnitude mass drop, clumping signatures, and no dust formation.
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MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance
MorphoFlow learns compact probabilistic 3D shape representations from sparse annotations using neural implicits, autodecoders, autoregressive flows, and adaptive sparsity priors on latent dimensions.
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Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models
VaFES constructs a latent space from reversible collective variables and variationally optimizes a tractable-density generative model to produce a continuous free energy surface from which rare events are directly sampled.
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Flow-Based Conformal Predictive Distributions
Differentiable nonconformity scores induce flows that sample conformal prediction set boundaries, and mixing flows across levels produces conformal predictive distributions whose quantiles match the sets.
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Breaking the Resolution Barrier: Arbitrary-resolution Deep Image Steganography Framework
ARDIS enables arbitrary-resolution deep image steganography via frequency decoupling in hiding and latent-guided implicit reconstruction for blind recovery.
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Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory
RGFlow uses flow-based neural networks to learn bijective real-space RG transformations for the 2D phi^4 theory, identifying a Wilson-Fisher-like critical point and estimating the correlation length exponent.
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Steering Your Diffusion Policy with Latent Space Reinforcement Learning
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.
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Variational Sequential Optimal Experimental Design using Reinforcement Learning
vsOED uses a variational one-point reward and RL policy optimization to provide a lower bound on expected information gain for sequential experimental design, supporting nuisance parameters, implicit likelihoods, and multiple design goals.
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Guided Image Generation with Conditional Invertible Neural Networks
Proposes cINN architecture for conditional image generation that by construction yields diverse sharp samples, demonstrated on MNIST digit generation and image colorization with latent space manipulation.
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Bounding-Box Trajectories Matter for Video Anomaly Detection
TrajVAD shows that bounding-box trajectories modeled via normalizing flows can serve as a primary cue for video anomaly detection, with the trajectory-only variant achieving 87.7% AP on ShanghaiTech and best results on MSAD.
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UST-Hand: An Uncertainty-aware Spatiotemporal Point Cloud Interaction Network for 3D Self-supervised Hand Pose Estimation
UST-Hand is a self-supervised 3D hand pose estimation method using conditional normalizing flows for uncertainty-aware hypothesis sampling and probabilistic point cloud interactions to achieve up to 37.8% better MPVPE than prior self-supervised approaches on three datasets.
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TVRN: Invertible Neural Networks for Compression-Aware Temporal Video Rescaling
TVRN combines invertible wavelet-based networks with a surrogate gradient approximator and compression-aware asymmetric design to improve frame-rate rescaling quality under real codecs.
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Operator Spectroscopy of Trained Lattice Samplers
Operator projections of trained sampler functions in 2D phi^4 lattice theory decompose residuals into zero-mode Binder and finite-k correlator components, distinguishing flow-matching, diffusion, and normalizing-flow models.
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CONTRA: Conformal Prediction Region via Normalizing Flow Transformation
CONTRA generates sharp multi-dimensional conformal prediction regions by defining nonconformity scores as distances from the center in the latent space of a normalizing flow.
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STARFlow2: Bridging Language Models and Normalizing Flows for Unified Multimodal Generation
STARFlow2 presents an autoregressive flow-based architecture for unified multimodal text-image generation by interleaving a VLM stream with a TarFlow stream via residual skips and a unified latent space.
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Accelerating the Simulation of Ordinary Differential Equations Through Physics-Preserving Neural Networks
A neural network maps ODE states to a slow-evolving latent space with dynamics derived from the original equations via the chain rule, enabling accelerated simulations with fewer function calls.
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Conservative Flows: A New Paradigm of Generative Models
Conservative flows generate by running probability-preserving stochastic dynamics initialized at data points rather than noise, using corrected Langevin or predictor-corrector mechanisms on top of any pretrained flow model and showing gains on Swiss-roll, ImageNet-256 and Oxford Flowers-102.
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Robust Conditional Conformal Prediction via Branched Normalizing Flow
Branched Normalizing Flow improves conditional coverage robustness of conformal prediction under distribution shift by normalizing test inputs to the calibration distribution and mapping prediction sets back.
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Normalizing Flows with Iterative Denoising
iTARFlow augments normalizing flows with diffusion-style iterative denoising during sampling while preserving end-to-end likelihood training, reaching competitive results on ImageNet 64/128/256.
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OLLM: Options-based Large Language Models
OLLM models next-token generation as a latent-indexed set of options, enabling up to 70% math reasoning correctness versus 51% baselines and structure-based alignment via a compact latent policy.
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Lookahead Drifting Model
The lookahead drifting model improves upon the drifting model by sequentially computing multiple drifting terms that incorporate higher-order gradient information, leading to better performance on toy examples and CIFAR10.
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Dartmouth Stellar Evolution Emulator (DSEE) 1: Generative Stellar Evolution Model Database
DSEE is a flow-based emulator that generates stellar evolution tracks and isochrones as probabilistic outputs from a single model trained on millions of simulations, enabling fast interpolation and uncertainty-aware analyses.
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Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation
Jeffreys Flow distills Parallel Tempering trajectories via Jeffreys divergence to produce robust Boltzmann generators that suppress mode collapse and correct sampling inaccuracies for rare event sampling.
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Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation
DBR-AF decouples cross-variable correlations in reconstruction and applies autoregressive flows to model residual densities for improved anomaly detection in multivariate time series.
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MPDiT: Multi-Patch Global-to-Local Transformer Architecture For Efficient Flow Matching and Diffusion Model
MPDiT uses a hierarchical multi-patch design in transformers to lower computation in diffusion models by handling coarse global features first then fine local details, plus faster-converging embeddings.
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Conditional flow matching for physics-constrained inverse problems with finite training data
Conditional flow matching learns a velocity field to sample from measurement-conditioned posteriors in physics inverse problems, with early stopping to prevent variance collapse and selective memorization under finite training data.
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Inferring the population properties of galactic binaries from LISA's stochastic foreground
A neural posterior estimator trained on simulated LISA foreground spectra recovers galactic binary population parameters, including total number, with good accuracy in validation tests.
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The Ensemble Schr{\"o}dinger Bridge filter for Nonlinear Data Assimilation
The Ensemble Schrödinger Bridge filter adds a diffusion-based analysis step to ensemble prediction, enabling effective nonlinear data assimilation without structural model error or training.
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RefTon: Reference person shot assist virtual Try-on
RefTon is a flux-based virtual try-on method that uses unpaired reference images of the target garment on different people to guide texture and detail preservation in a streamlined person-to-person pipeline without body parsing or masks.
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Marginal Girsanov Reweighting: Stable Variance Reduction for Long-Timescale Dynamics from Biased Simulation
Marginal Girsanov Reweighting stabilizes variance by marginalizing over intermediate paths to enable reliable reweighting of long-timescale dynamics from biased molecular simulations.
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Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling
Energy-Weighted Flow Matching reformulates conditional flow matching with importance sampling to enable continuous normalizing flows to model Boltzmann distributions from energy evaluations alone, with iterative and annealed variants showing competitive performance on benchmarks.
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Improving the Accuracy of Amortized Model Comparison with Self-Consistency
Self-consistency training on real data improves amortized Bayesian model comparison accuracy under distribution shifts, especially in open-world misspecification when analytic or locally accurate surrogate likelihoods are available.
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TabICL: A Tabular Foundation Model for In-Context Learning on Large Data
TabICL scales in-context learning to large tabular data via column-then-row attention for row embeddings followed by a transformer, matching TabPFNv2 speed and performance while outperforming it and CatBoost on datasets over 10K samples.
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Density Estimation via Binless Multidimensional Integration
BMTI estimates log-density via integration of neighbor differences on data manifolds using maximum-likelihood weighting, without binning or explicit coordinates.
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ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection
ConjNorm reframes OOD detection score design as optimizing norm p in an exponential family density model via a Bregman divergence theorem, with a tractable Monte Carlo estimator, claiming SOTA gains on CIFAR-100 and ImageNet-1K.
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DragNUWA: Fine-grained Control in Video Generation by Integrating Text, Image, and Trajectory
DragNUWA integrates text, image, and trajectory controls into a diffusion video model using a Trajectory Sampler, Multiscale Fusion, and Adaptive Training to enable fine-grained open-domain video generation.
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Rectified Flow: A Marginal Preserving Approach to Optimal Transport
A single-objective rectified flow variant uses neural ODEs trained by regression to monotonically decrease a fixed convex transport cost while preserving marginal distributions.