Generative Modelling With Inverse Heat Dissipation

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the desirability of coarse-to-fine modelling, we propose a new model that generates images through iteratively inverting the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. In our novel methodology, the solution of the forward heat equation is interpreted as a variational approximation in a directed graphical model. We demonstrate promising image quality and point out emergent qualitative properties not seen in diffusion models, such as disentanglement of overall colour and shape in images and aspects of neural network interpretability. Spectral analysis on natural images positions our model as a type of dual to diffusion models and reveals implicit inductive biases in them.