Diffusion Models for Multifractal Texture Synthesis

Multifractal textures provide a robust framework for modeling real-world textures characterized by complex, transient, and statistically rich patterns, with applications spanning biomedical imaging to material science. While diffusion models have proven effective in generative tasks, their ability to synthesize textures, i.e., images with no geometry but instead with rich and complex spatial dynamics, remains underexplored. This study investigates the performance of diffusion neural networks in generating multifractal textures, which are used as representatives of such complex textures with prescribed statistical properties, yet without embedding multifractal information in the training loss. From a dataset of 1000 multifractal textures, a U-Net-based diffusion model is trained, under four different noise schedulers to explore their influence on synthesis quality. Performance is evaluated by comparing the multifractal statistics, assessed by wavelet-leader analysis, of generated textures against those of the training set. Results suggest that overall the linear noise scheduler performs best in reproducing multifractal properties in textures.