arXiv:2605. 05629v3 Announce Type: replace-cross Abstract: We study the problem of learning generative models for discrete sequences in a continuous embedding space.
arXiv:2605. 13352v2 Announce Type: replace Abstract: Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support).
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:2605. 11125v3 Announce Type: replace Abstract: Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities.
arXiv:2506. 21278v3 Announce Type: replace-cross Abstract: We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces.
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
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 the spherical Cauchy distribution as a new hyperspherical posterior for variational autoencoders, avoiding the complications of the von Mises–Fisher and Power Spherical alternatives. By using stereographic projection and a Möbius transformation, the authors obtain exact posterior samples and a closed‑form KL divergence that terminates in a finite polynomial for even dimensions and admits certified truncation for odd dimensions. Empirical results show that the spherical Cauchy yields faster inference and lower reconstruction loss on MNIST and improved negative log‑likelihood on smallNORB compared to existing methods.
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
arXiv:2609.05727v1 Announce Type: cross Abstract: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $\pi\propto\mu e^{\tau r}$, where...
The paper addresses a flaw in latent‑variable generative models on Riemannian manifolds such as spheres and hyperbolic spaces, where the usual practice of sampling a Gaussian in a tangent space and mapping it onto the manifold inadvertently imposes a fixed chi‑distribution on distances from a base point. The authors formulate and solve the inverse problem: given a desired distance distribution, they derive the exact tangent‑space density that yields it, prove its uniqueness for isotropic, chart‑independent likelihoods, and provide a lower bound on the cost of ignoring this issue in variational autoencoders. Experiments with exact normalization audits show that the compensated prior is chart‑invariant, stable across scales, and leads to significant improvements in curvature recovery and protein‑orientation likelihoods. whyItMatters":"By correcting the implicit distance distribution, the method enables more accurate and stable generative modeling on curved spaces, directly improving performance on tasks such as protein orientation."
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.