Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
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abstract
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called stochastic interpolants to bridge any two probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent density function of the interpolant is shown to satisfy a transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also construct estimators for the likelihood and the cross entropy of interpolant-based generative models, and we discuss connections with other methods such as score-based diffusion models, stochastic localization, probabilistic denoising, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.
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- abstract A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called stochastic interpolants to bridge any two probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent density function of the interpolant is shown to satisfy a transport e
co-cited works
representative citing papers
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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.
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising methods on three benchmarks.
Linear-DPO replaces sigmoid utility with linear utility and adds EMA reference to improve preference alignment in diffusion and flow-matching text-to-image models.
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
A generative transfer framework using iterative path-wise tilting integrated with conditional flow matching recovers target entropic optimal transport couplings from reference samples, achieving O(δ) convergence in Wasserstein-1 distance.
Non-monotonic sampling schedules never improve upon monotonic baselines in diffusion models, with performance gaps ranging from substantial to negligible depending on the denoiser.
TMPO uses Softmax Trajectory Balance to match policy probabilities over multiple trajectories to a Boltzmann reward distribution, improving diversity by 9.1% in diffusion alignment tasks.
FLUX reconstructs longitudinal transport and recovers interpretable regime structure from unpaired biological snapshots by combining geometry-aware flow matching with mixture-of-experts velocity decomposition.
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
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.
ABC enables any-subset autoregressive generation of continuous stochastic processes via non-Markovian diffusion bridges that track physical time and allow path-dependent conditioning.
ALMC-ODE uses annealed Langevin Monte Carlo with Jarzynski reweighting to produce a low-variance velocity estimator for flow ODE sampling, with an O(1/n) MSE bound and superior performance on multimodal benchmarks.
ScoRe-Flow achieves decoupled mean-variance control in stochastic flow matching by deriving a closed-form score for drift modulation plus learned variance, yielding faster RL convergence and higher success rates on locomotion and manipulation benchmarks.
GVCC achieves the lowest LPIPS on UVG at bitrates down to 0.003 bpp by encoding stochastic innovations in a marginal-preserving stochastic process derived from a pretrained rectified-flow video model, with 65% LPIPS reduction over DCVC-RT.
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.
A neural path estimation approach learns the filtering posterior path measure for stochastic dynamical systems from noisy partial observations by solving a variational stochastic control problem based on the pathwise Zakai equation.
A geometric latent-subspace model on Riemannian manifolds of categorical distributions enables low-dimensional generative modeling of discrete data via isometries and geometric PCA for flow matching.
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.
SCSI iteratively refines a self-consistent transport map to invert black-box corruptions and enable generative modeling of clean data.
Flow matching models follow a two-stage process of navigation across data modes then refinement to nearest samples, revealed by exact computation of the oracle marginal velocity field.
FMA introduces flow matching for multi-step cross-modal feature alignment in few-shot learning, using fixed coupling, noise augmentation, and early-stopping to outperform one-step PEFT methods.
Minimizing averaged squared Lipschitzness of the drift produces interpolation schedules that improve numerical accuracy and mitigate mode collapse in generative models, with closed-form optima for Gaussians and validation on stochastic PDEs.
citing papers explorer
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Is Flow Matching Just Trajectory Replay for Sequential Data?
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.
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Generative Modeling of Discrete Data Using Geometric Latent Subspaces
A geometric latent-subspace model on Riemannian manifolds of categorical distributions enables low-dimensional generative modeling of discrete data via isometries and geometric PCA for flow matching.
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On The Hidden Biases of Flow Matching Samplers
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.
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Lipschitz-Guided Design of Interpolation Schedules in Generative Models
Minimizing averaged squared Lipschitzness of the drift produces interpolation schedules that improve numerical accuracy and mitigate mode collapse in generative models, with closed-form optima for Gaussians and validation on stochastic PDEs.
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Flow Matching is Adaptive to Manifold Structures
Flow matching achieves near-minimax optimal statistical consistency for manifold-supported distributions, with convergence rates governed by intrinsic dimension and smoothness rather than ambient dimension.
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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.