Adapting Noise to Data: Generative Flows from learned 1D Processes

Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl

Keywords: generative modelling, flow matching, noise learning, optimal transport

Abstract:

We introduce a general framework for learning data-adaptive latent distributions (noise)
in generative models based on 1D quantile functions through minimizing a statistical
discrepancy between noise and data samples. Our quantile-based parameterization naturally
adapts to heavy-tailed or compactly supported target distributions while shortening transport
paths by capturing marginal structure. This construction, originally motivated by the study
of 1D processes beyond the usual diffusion, integrates seamlessly with standard training
objectives, including flow matching and consistency models. Numerical experiments
highlight both the flexibility and the effectiveness of our approach, achieved with minimal
computational overhead.

Primary Area: generative models

Submission Number: 13384