Shaping Inductive Bias in Diffusion Models through Frequency-Based Noise Control

TL;DR

This paper introduces a frequency-based noising operator for diffusion probabilistic models to incorporate inductive biases, improving their focus on specific data aspects and enhancing generative performance, especially in structured data scenarios.

Contribution

It proposes a novel frequency-based noise control method to shape inductive biases in diffusion models, tailored for topologically structured data, and demonstrates improved performance over standard approaches.

Findings

Frequency-based noise control enhances generative quality.

Different datasets require different inductive biases.

Ignoring certain frequencies can improve learning in corrupted data recovery.

Abstract

Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model. For topologically structured data, we devise a frequency-based noising operator to purposefully manipulate, and set, these inductive biases. We first show that appropriate manipulations of the noising forward process can lead DPMs to focus on particular aspects of the distribution to learn. We show that different datasets necessitate different inductive biases, and that appropriate frequency-based noise control induces increased generative performance compared to standard diffusion. Finally, we demonstrate the possibility of ignoring information at particular frequencies while learning. We show this in an image corruption and recovery task, where we train a DPM to recover the original target distribution after severe noise corruption.