Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
arXiv preprint arXiv:2211.01364 (2022)
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A McKean-Vlasov FBSDE generative model learns stochastic path laws that match observed terminal and time-marginal distributions via soft energy constraints rather than hard interpolation.
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.
Gaussian mixture models combined with multiple local linearizations solve nonlinear stochastic density steering and yield provably tighter approximation bounds than single-linearization baselines.
A forward-backward HJB duality computes the optimal stochastic transport control from easy forward relaxation trajectories alone, expressed as path-space free energy without backward simulation.
Adjoint matching objectives derived from the Stochastic Maximum Principle have critical points satisfying HJB stationarity conditions for SOC problems with control-dependent drift and diffusion.
SOCS derives per-step closed-form control signals from stochastic optimal control to steer diffusion sampling trajectories toward measurements while preserving the generative prior.
E-Bridge approximates low-cost geodesic trajectories in diffusion bridges for image restoration by using shorter time horizons, entropy-regularized starts mixing degraded images with noise, and consistency-model single-step mapping, achieving SOTA results with one or few steps.
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Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
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Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach
A McKean-Vlasov FBSDE generative model learns stochastic path laws that match observed terminal and time-marginal distributions via soft energy constraints rather than hard interpolation.
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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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Nonlinear Stochastic Density Steering via Gaussian Mixture Schrodinger Bridges and Multiple Linearizations
Gaussian mixture models combined with multiple local linearizations solve nonlinear stochastic density steering and yield provably tighter approximation bounds than single-linearization baselines.
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Generative optimal transport via forward-backward HJB matching
A forward-backward HJB duality computes the optimal stochastic transport control from easy forward relaxation trajectories alone, expressed as path-space free energy without backward simulation.
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Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control
Adjoint matching objectives derived from the Stochastic Maximum Principle have critical points satisfying HJB stationarity conditions for SOC problems with control-dependent drift and diffusion.
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Stochastic Optimal Control Sampling for Diffusion Inverse Problems
SOCS derives per-step closed-form control signals from stochastic optimal control to steer diffusion sampling trajectories toward measurements while preserving the generative prior.
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Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models
E-Bridge approximates low-cost geodesic trajectories in diffusion bridges for image restoration by using shorter time horizons, entropy-regularized starts mixing degraded images with noise, and consistency-model single-step mapping, achieving SOTA results with one or few steps.
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