Uncovering the Generative Landscape of Diffusion Models: A Spectral-Guided Quality-Diversity Diffusion Framework

Denoising Diffusion Probabilistic Models have emerged as powerful generative priors across domains ranging from molecular design to high-resolution image synthesis. However, standard diffusion sampling is inherently biased toward high-likelihood regions, often limiting the diversity of outputs. In many domains, a single, high-likelihood sample is insufficient. Instead, diverse portfolios of high-performing solutions are required, motivating methods that uncover a model's full expressive range. Here we show that integrating Quality-Diversity (QD) optimisation with diffusion models enables the discovery of diverse, high-performing outputs. We first propose Quality-Diversity Diffusion, a framework that adapts QD to diffusion models by directly optimising the model's latent noise and conditioning embeddings and leveraging embedding models to quantify diversity. Second, we introduce a novel h-space Spectral Mutation operator, which guides search along directions of maximal semantic sensitivity by analysing principal singular vectors of the model's input-to-activation Jacobian. We evaluate our combined approach, Spectral-Guided Quality-Diversity Diffusion, on text-to-image generation. Against $12$ baselines, our method consistently achieves the lowest FID score, demonstrating an excellent balance of image quality and diversity.