FGM-HD: Boosting Generation Diversity of Fractal Generative Models through Hausdorff Dimension Induction

The introduction of FGM-HD marks a significant advancement in the field of image generation, particularly in overcoming the limitations posed by Fractal Generative Models (FGMs). These models, while efficient in producing high-quality images, often suffer from a lack of diversity due to their inherent self-similarity. The novel approach proposed in the study utilizes the Hausdorff Dimension (HD) to quantify and enhance structural complexity in generated images. By implementing a learnable HD estimation method and an HD-based loss with a monotonic momentum-driven scheduling strategy, the researchers successfully optimized hyperparameters during training. This resulted in a remarkable 39% increase in output diversity without compromising visual quality, as demonstrated through extensive experiments on the ImageNet dataset. The findings not only address a critical challenge in image generation but also pave the way for future developments in generating diverse and high-quality images.