arXiv subjects

Jannis Chemseddine

Publications and source records attributed to Jannis Chemseddine.

8 recordsLinked to original sources

arXiv2026

Spherical Flows for Sampling Categorical Data

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on $(\mathbb S^{d-1})^L$ both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The vMF path especially in combination with PC sampling significantly improves results on Sudoku, language modeling, and mathematical reasoning.

stat.ML↗

arXiv2026

Self-Aware Markov Models for Discrete Reasoning

Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their computation to the complexity of a given problem. To address these limitations, we introduce a method based on learning a Markov transition kernel that is trained on its own outputs. This design enables tokens to be remasked, allowing the model to correct its previous mistakes. Furthermore, we do not need a fixed time schedule but use a trained stopping criterion. This allows for adaptation of the number of function evaluations to the difficulty of the reasoning problem. Our adaptation adds two lightweight prediction heads, enabling reuse and fine-tuning of existing pretrained models. On the Sudoku-Extreme dataset we clearly outperform other flow based methods with a validity of 95%. For the Countdown-4 we only need in average of 10 steps to solve almost 96% of them correctly, while many problems can be solved already in 2 steps.

cs.LG↗

arXiv2025

Adapting Noise to Data: Generative Flows from 1D Processes

The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method's flexibility and effectiveness achieved with negligible computational overhead.

stat.ML↗

arXiv2025

Telegrapher's Generative Model via Kac Flows

We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equation and Brownian motion, there is a Feynman-Kac type relation between the telegrapher's equation and the stochastic Kac process in 1D. The Kac flow evolves stepwise linearly in time, so that the probability flow is Lipschitz continuous in the Wasserstein distance and, in contrast to diffusion flows, the norm of the velocity remains globally bounded. Furthermore, the Kac model has the diffusion model as its asymptotic limit. We extend these considerations to a multi-dimensional stochastic process which consists of independent 1D Kac processes in each spatial component. We show that this process gives rise to an absolutely continuous curve in the Wasserstein space and analytically compute the conditional velocity field when starting in a Dirac point. Using the framework of flow matching, we train a neural network to approximate the velocity field and use it for sample generation. Our numerical experiments demonstrate the scalability of our approach, and show its advantages over diffusion models.

math.AP↗

arXiv2024

Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometry

We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are absolutely continuous in the Wasserstein geometry. Second, we address specific interpolations $f_t$ and the learning of the related density/velocity pairs $(\rho_t,v_t)$. It was numerically observed that the linear interpolation, which requires only a parametrization of the velocity field $v_t$, suffers from a "teleportation-of-mass" issue. Using tools from the Wasserstein geometry, we give an analytical example, where we can precisely measure the explosion of the velocity field. Inspired by M\'at\'e and Fleuret, who parametrize both $f_t$ and $v_t$, we propose an interpolation which parametrizes only $f_t$ and fixes an appropriate $v_t$. This corresponds to the Wasserstein gradient flow of the Kullback-Leibler divergence related to Langevin dynamics. We demonstrate by numerical examples that our model provides a well-behaved flow field which successfully solves the above sampling task.

cs.LG↗

arXiv2024

Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior measures in the case of the Kullback--Leibler divergence, this is in general not hold true for the Wasserstein distance. In this paper, we introduce a conditional Wasserstein distance via a set of restricted couplings that equals the expected Wasserstein distance of the posteriors. Interestingly, the dual formulation of the conditional Wasserstein-1 flow resembles losses in the conditional Wasserstein GAN literature in a quite natural way. We derive theoretical properties of the conditional Wasserstein distance, characterize the corresponding geodesics and velocity fields as well as the flow ODEs. Subsequently, we propose to approximate the velocity fields by relaxing the conditional Wasserstein distance. Based on this, we propose an extension of OT Flow Matching for solving Bayesian inverse problems and demonstrate its numerical advantages on an inverse problem and class-conditional image generation.

cs.LG↗

arXiv2023

Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior measures in the case of the Kullback Leibler divergence, it does not hold true for the Wasserstein distance. We will introduce a conditional Wasserstein distance with a set of restricted couplings that equals the expected Wasserstein distance of the posteriors. By deriving its dual, we find a rigorous way to motivate the loss of conditional Wasserstein GANs. We outline conditions under which the vanilla and the conditional Wasserstein distance coincide. Furthermore, we will show numerical examples where training with the conditional Wasserstein distance yields favorable properties for posterior sampling.

cs.LG↗

arXiv2023

Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

stat.ML↗