publications

Current Work

2026

1. One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators

   P. Tsimpos, E. Calvello, A. Belhadji, and 1 more author

   In arXiv, 2026

   Preprint

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   Probabilistic conditioning is concerned with the identification of a distribution of a random variable X given a random variable Y. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This problem has traditionally been addressed in machine learning by directly learning the conditional distribution of a fixed joint distribution. This paper introduces a novel perspective: we propose to solve the conditioning problem by identifying a single operator that maps any joint density to its conditional, thus amortizing over joint-conditional pairs. We establish that the conditioning operator can be approximated to arbitrary accuracy by neural operators. Our proof relies on new results establishing continuity of the conditioning operator over suitable classes of densities. Finally, we learn the conditioning map for a class of Gaussian mixtures using neural operators, illustrating the promise of our framework. This work provides the theoretical underpinnings for general-purpose, amortized methods for probabilistic conditioning, such as foundation models for Bayesian inference.

2. One-Shot Generative Flows: Existence and Obstructions

   P. Tsimpos, D. Sharp, and Y. M. Marzouk

   In arXiv, 2026

   Preprint

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   We study dynamic measure transport for generative modelling in the setting of a stochastic process X_∙whose marginals interpolate between a source distribution P_0 and a target distribution P_1 while remaining independent, i.e., when (X_0,X_1)∼P_0⊗P_1. Conditional expectations of this process X_∙define an ODE whose flow map transports from P_0 to P_1. We discuss when such a process induces a \emphstraight-line flow, namely one whose pointwise acceleration vanishes and is therefore exactly integrable by any first-order method. We first develop multiple characterizations of straightness in terms of PDEs involving the conditional statistics of the process. Then, we prove that straightness under endpoint independence exhibits a sharp dichotomy. On one hand, we construct explicit, computable straight-line processes for arbitrary Gaussian endpoints. On the other hand, we show straight-line processes do not exist for targets with sufficiently well-separated modes. We demonstrate this through a sequence of increasingly general impossibility theorems that uncover a fundamental relationship between the sample-path behavior of a process with independent endpoints and the space-time geometry of this process’ flow map. Taken together, these results provide a structural theory of when straight generative flows can, and cannot, exist.

2025

1. An Eulerian Perspective on Straight-Line Sampling

   P. Tsimpos and Y. M. Marzouk

   In 2nd edition of Frontiers in Probabilistic Inference: Learning meets Sampling, Nov 2025

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   We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process’ velocity defines an ODE whose flow map achieves the desired transport. We ask \emphwhich processes produce straight-line flows – i.e., flows whose pointwise acceleration vanishes and thus are exactly integrable with a first-order method? We provide a concise PDE characterization of straightness as a balance between conditional acceleration and the divergence of a weighted covariance (Reynolds) tensor. Using this lens, we fully characterize affine-in-time interpolants and show that straightness occurs exactly under deterministic endpoint couplings. We also derive necessary conditions that constrain flow geometry for general processes, offering broad guidance for designing transports that are easier to integrate.

2. Optimal Scheduling of Dynamic Transport

   P. Tsimpos, Z. Ren, J. Zech, and 1 more author

   In Proceedings of Thirty Eighth Conference on Learning Theory, Jun 2025

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   Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a transport map that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this freedom. Though many popular methods seek straight line (i.e., zero acceleration) trajectories, we show here that a specific class of “curved” trajectories can significantly improve approximation and learning. In particular, we consider the unit-time interpolation of any given transport map T and seek the schedule τ:[0,1]→[0,1] that minimizes the spatial Lipschitz constant of the corresponding velocity field over all times t∈[0,1]. This quantity is crucial as it allows for control of the approximation error when the velocity field is learned from data. We show that, for a broad class of source/target measures and transport maps T, the \emphoptimal schedule can be computed in closed form, and that the resulting optimal Lipschitz constant is \emphexponentially smaller than that induced by an identity schedule (corresponding to, for instance, the Wasserstein geodesic). Our proof technique relies on the calculus of variations and Γ-convergence, allowing us to approximate the aforementioned degenerate objective by a family of smooth, tractable problems.

Past Work

2025

1. Hybrid machine learning for real-time prediction of edema trajectory in large middle cerebral artery stroke

   Ethan Phillips, Odhran O’Donoghue, Yumeng Zhang, and 8 more authors

   npj Digital Medicine, 2025

2024

1. HELMET: A Hybrid Machine Learning Framework for Real-Time Prediction of Edema Trajectory in Large Middle Cerebral Artery Stroke

   Ethan Phillips, Odhran O’Donoghue, Yumeng Zhang, and 8 more authors

   medRxiv, 2024