Hyperbolic Curvature as an Inductive Bias for Latent Space Flow Matching

Federica Valeau, Maria Esteban-Casadevall, Erik J Bekkers

Track: tiny paper (up to 4 pages)

Keywords: Riemannian flow matching, hyperbolic autoencoders, geometric inductive bias, image generation

TL;DR: We propose a framework that combines flow matching with the latent space of a hyperbolic autoencoder, investigating how latent geometry influences generative transport.

Abstract: Learning image representations that respect the intrinsic geometry of data is crucial for capturing hierarchical semantic structure, yet generative transport is typically performed in Euclidean spaces where this structure is not preserved. In this work, we propose a geometry-aware generative framework that combines hyperbolic representation learning with Riemannian Flow Matching to perform generative transport directly in hyperbolic latent space. Instead of learning generative dynamics in pixel space or Euclidean latents, we transport samples directly on the manifold produced by a pretrained hyperbolic autoencoder, preserving geometric organization and yielding more stable samples than Euclidean latent transport. We further investigate curvature as a controllable geometric inductive bias and observe a trade-off between generation realism and diversity, where moderate curvature yields more coherent samples, and larger curvature allows visual variation at the cost of stability, highlighting how latent geometry shapes generative transport.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Presenter: ~Federica_Valeau1

Format: Yes, the presenting author will definitely attend in person because they attending ICLR for other complementary reasons.

Funding: Yes, the presenting author of this submission falls under ICLR’s funding aims, and funding would significantly impact their ability to attend the workshop in person.

Serve As Reviewer: ~Federica_Valeau1

Submission Number: 111