Adapting Noise to Data: Generative Flows from 1D Processes
This work addresses the challenge of flexible generative modeling for machine learning researchers, offering an incremental improvement by making noise processes learnable within existing frameworks.
The authors tackled the problem of constructing generative models by introducing a framework where one-dimensional noising processes are learnable through quantile functions that adapt to data, resulting in a method that captures heavy tails and compact supports effectively.
We introduce a general framework for constructing generative models using one-dimensional noising processes. Beyond diffusion processes, we outline examples that demonstrate the flexibility of our approach. Motivated by this, we propose a novel framework in which the 1D processes themselves are learnable, achieved by parameterizing the noise distribution through quantile functions that adapt to the data. Our construction integrates seamlessly with standard objectives, including Flow Matching and consistency models. Learning quantile-based noise naturally captures heavy tails and compact supports when present. Numerical experiments highlight both the flexibility and the effectiveness of our method.