Stochastic interpolants unify flow-based and diffusion-based generative models by bridging target densities exactly via latent-variable processes whose drifts minimize quadratic objectives.
Monge-Amp\`ere Flow for Generative Modeling
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\`ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\`ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.
verdicts
UNVERDICTED 4representative citing papers
URGE performs unbiased inference-time scaling for diffusion models by attaching multiplicative path weights from Girsanov estimation and resampling trajectories, with a proven equivalence to prior particle-wise SMC schemes.
FES-FM applies reduced flow matching with a Hessian-derived prior to directly sample free energy surfaces in collective variable space, claiming lower computational cost and higher accuracy per unit time than standard methods.
Neural networks learn the score of the probability density on Bohmian trajectories to recover exact Schrödinger dynamics via self-consistent minimization for nodeless wave functions, demonstrated on double-well splitting and Morse chain vibrations.
citing papers explorer
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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Stochastic interpolants unify flow-based and diffusion-based generative models by bridging target densities exactly via latent-variable processes whose drifts minimize quadratic objectives.
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Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures
URGE performs unbiased inference-time scaling for diffusion models by attaching multiplicative path weights from Girsanov estimation and resampling trajectories, with a proven equivalence to prior particle-wise SMC schemes.
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Free Energy Surface Sampling via Reduced Flow Matching
FES-FM applies reduced flow matching with a Hessian-derived prior to directly sample free energy surfaces in collective variable space, claiming lower computational cost and higher accuracy per unit time than standard methods.
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Quantum Dynamics via Score Matching on Bohmian Trajectories
Neural networks learn the score of the probability density on Bohmian trajectories to recover exact Schrödinger dynamics via self-consistent minimization for nodeless wave functions, demonstrated on double-well splitting and Morse chain vibrations.