6 citations · 34 across the 26 of their papers we have counts for
28 papers
Learning smooth dynamics via Kinematic Interpolants
Yiheng, Jiang, Youssef Marzouk +2
Inferring dynamics from real-world experimental data is inherently ambiguous, as many plausible dynamical systems can explain the same positional observations at measurement times.…
Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime
Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian +2
Modern score-based generative models have achieved remarkable empirical success in high-dimensional tasks such as image, audio, and video synthesis. These models reduce distributio…
Trajectory inference via Acceleration Matching
Bartolo Dazzini, Giovanni Conforti, Alain Durmus +1
Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate…
Near-Lipschitz stability of the Kim--Milman flow map
Sinho Chewi, Katharina Eichinger, Aram-Alexandre Pooladian
We prove that the Kim--Milman flow map enjoys favorable stability properties with respect to variations in the target measure, provided that one of the target measures is sufficien…
Variational inference via radial transport
Luca Ghafourpour, Sinho Chewi, Alessio Figalli +1
In variational inference (VI), the practitioner approximates a high-dimensional distribution with a simple surrogate one, often a (product) Gaussian distribution. However, in m…
Blind denoising diffusion models and the blessings of dimensionality
Zahra Kadkhodaie, Aram-Alexandre Pooladian, Sinho Chewi +1
Denoising diffusion models (DDMs) are state-of-the-art methods for learning densities from data across numerous domains, yet many aspects of the training and sampling pipeline rema…
Theory and computation for structured variational inference
Shunan Sheng, Bohan Wu, Bennett Zhu +2
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to…
Stability of the Kim--Milman flow map
Sinho Chewi, Aram-Alexandre Pooladian, Matthew S. Zhang
In this short note, we characterize stability of the Kim--Milman flow map -- also known as the probability flow ODE -- with respect to variations in the target measure in relative…
Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier maps
Ricardo Baptista, Aram-Alexandre Pooladian, Michael Brennan +2
Conditional simulation is a fundamental task in statistical modeling: Generate samples from the conditionals given finitely many data points from a joint distribution. One promisin…
Wasserstein Flow Matching: Generative modeling over families of distributions
Doron Haviv, Aram-Alexandre Pooladian, Dana Pe'er +1
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics an…
Plug-in estimation of Schrödinger bridges
Aram-Alexandre Pooladian, Jonathan Niles-Weed
We propose a procedure for estimating the Schrödinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating f…
Progressive Entropic Optimal Transport Solvers
Parnian Kassraie, Aram-Alexandre Pooladian, Michal Klein +3
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds…
Neural Optimal Transport with Lagrangian Costs
Aram-Alexandre Pooladian, Carles Domingo-Enrich, Ricky T. Q. Chen +1
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagra…
Tight stability bounds for entropic Brenier maps
Vincent Divol, Jonathan Niles-Weed, Aram-Alexandre Pooladian
Entropic Brenier maps are regularized analogues of Brenier maps (optimal transport maps) which converge to Brenier maps as the regularization parameter shrinks. In this work, we pr…
Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space
Yiheng Jiang, Sinho Chewi, Aram-Alexandre Pooladian
We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is t…
Learning Elastic Costs to Shape Monge Displacements
Michal Klein, Aram-Alexandre Pooladian, Pierre Ablin +3
Given a source and a target probability measure supported on , the Monge problem asks to find the most efficient way to map one distribution to the other. This effici…
Multisample Flow Matching: Straightening Flows with Minibatch Couplings
Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich +3
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, su…
An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flow
Carles Domingo-Enrich, Aram-Alexandre Pooladian
Let be some (possibly non-convex) potential function, and consider the probability measure . When exhibits multiple modes…
Minimax estimation of discontinuous optimal transport maps: The semi-discrete case
Aram-Alexandre Pooladian, Vincent Divol, Jonathan Niles-Weed
We consider the problem of estimating the optimal transport map between two probability distributions, and in , on the basis of i.i.d. samples. All existing st…
Optimal transport map estimation in general function spaces
Vincent Divol, Jonathan Niles-Weed, Aram-Alexandre Pooladian
We study the problem of estimating a function given independent samples from a distribution and from the pushforward distribution . This setting is motivated by…
An entropic generalization of Caffarelli's contraction theorem via covariance inequalities
Sinho Chewi, Aram-Alexandre Pooladian
The optimal transport map between the standard Gaussian measure and an -strongly log-concave probability measure is -Lipschitz, as first observed in a celebrated theor…
Debiaser Beware: Pitfalls of Centering Regularized Transport Maps
Aram-Alexandre Pooladian, Marco Cuturi, Jonathan Niles-Weed
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures and is a problem fraught with computational and statistical challenges. A promising approach…
Entropic estimation of optimal transport maps
Aram-Alexandre Pooladian, Jonathan Niles-Weed
We develop a computationally tractable method for estimating the optimal map between two distributions over with rigorous finite-sample guarantees. Leveraging an ent…
A Study of One-Parameter Regularization Methods for Mathematical Programs with Vanishing Constraints
Tim Hoheisel, Blanca Pablos, Aram-Alexandre Pooladian +2
Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology des…