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. This study investigates the capability of diffusion neural networks to synthesize univariate multifractal random walk (MRW) textures, using a UNet-based model trained on 1000 textures with fixed parameters (Hurst exponent $H=0.8$, multifractality parameter $\lambda^2=0.01$). Four noise schedulers—linear, cosine, quadratic, and sigmoid—are evaluated for their ability to reproduce global correlation ($C_1(2^j)$) and multifractal properties ($C_2(2^j)$) through wavelet-leader-based multifractal analysis. The linear scheduler demonstrates superior performance, closely reproducing the global scaling properties and inducing multifractality with high fidelity and low variability, though not perfectly matching the training data’s multifractal intensity. The findings highlight the potential of diffusion models for texture synthesis and suggest avenues for future work, including extending the approach to multivariate multifractal textures and designing specialized architectures to better capture intricate statistical structures.

Recommended citation: Abbas, Kinan, Abry, Patrice, and Roux, Stephane. (2025). "Diffusion Models for Multifractal Texture Synthesis." In Proceedings of the European Signal Processing Conference (EUSIPCO).
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