The paper presents Variational Doob-Wasserstein Flow (VDWF), a simulation-free method for learning unbalanced population dynamics on the Riemannian Wasserstein-Fisher-Rao manifold. VDWF first learns a geometry model with a data-dependent metric to capture intrinsic dynamics, then uses Doob's h-transform to incorporate boundary information for trajectory inference. It employs a growth model to learn dynamics and construct intermediate mass samples in WFR space, analyzes convergence via a uniform Log-Sobolev inequality, and demonstrates competitive performance on real-world datasets for both balanced and unbalanced dynamics.
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.
The paper introduces Double‑Stitch, a simulation‑free method for learning population dynamics in Wasserstein space. It penalizes the residual of the equation of motion along a learned path, derived from a Clebsch variational principle that avoids gradient velocities. Experiments on synthetic, single‑cell, and ocean vortex data show that Double‑Stitch matches or surpasses gradient‑flow and simulation‑based methods while training 4–14 times faster.
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
arXiv:2610.10278v1 Announce Type: cross Abstract: We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kin...
arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
arXiv:2609.25659v1 Announce Type: new Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
The paper introduces SUDO, a simulation‑free framework for unbalanced dynamic optimal transport (UDOT) that supports general convex growth penalties beyond the quadratic Wasserstein‑Fisher‑Rao case. By showing that concave penalties lead to degenerate solutions, the authors focus on convex penalties, learning conditional paths and transport costs to solve a semi‑coupling problem and then applying unbalanced flow matching. On benchmark datasets, SUDO matches the accuracy of analytical WFR solvers while being faster than simulation‑based methods, and it also handles asymmetric penalties that better reflect proliferation‑dominant biological priors.
arXiv:2603. 10718v3 Announce Type: replace Abstract: Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE.
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
arXiv:2611.05605v1 Announce Type: new Abstract: Variational approaches to learning transport maps for multimodal sampling can suffer from mode collapse. One way to mitigate this problem is to learn t...