Fractional Diffusion for Dinosaur Image Generation

Generative modeling of dinosaur imagery is challenging due to large inter-species morphological variation, complex textures (scales, skin folds, armour, horns), and limited curated datasets. This paper investigates diffusion-based image generation for dinosaur images using a Denoising Diffusion Probabilistic Models (DDPM) and introduces fractional-order image analysis as a principled tool for evaluating the quality of generated images. Experiments are conducted on a 15-species dinosaur image dataset derived from the Jurassic Park franchise, consisting of two thousand images spanning diverse body structures, postures, and visual styles.

A DDPM model is trained to generate dinosaur images from Gaussian noise using a U-Net–based denoiser. To assess generation quality beyond conventional pixel-wise or perceptual metrics, we employ fractional calculus–based texture and structure measures. Fractional-order gradients, fractional Laplacian energy, and fractional spectral statistics are computed on both real and generated images across a range of fractional orders. These metrics enable continuous interpolation between fine-scale texture sensitivity and coarse morphological structure, providing a richer characterization of generative fidelity than integer-order operators.

Quantitative analysis reveals that fractional-order metrics are highly sensitive to differences in textural realism, edge continuity, and long-range spatial correlations between real and synthetic images. An optimal fractional order is observed at which the statistical distributions of generated images most closely match those of real dinosaur images, particularly for species with distinctive skin patterns and skeletal outlines. Visual inspection further confirms that fractional-order analysis highlights improvements in fine-scale detail preservation as diffusion training progresses.

The results demonstrate that fractional calculus provides an effective and interpretable framework for evaluating diffusion-generated images, especially for complex, texture-rich objects such as dinosaurs. This work highlights the synergy between diffusion models and fractional-order image analysis, offering new directions for generative modelling assessment in data-limited scientific and educational image processing domains.