Enhancing diffusion models with Gaussianization preprocessing

Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have emerged as one of the most powerful classes of generative models for high-dimensional data, achieving state-of-the-art performance in image synthesis (Dhariwal and Nichol, 2021; Rombach et al., 2022) and other tasks such as action generation in robotic or protein design (Watson et al., 2023; Chi et al., 2025). However, sampling from these models is typically slow: many reverse-time steps are required to transform an initial Gaussian sample into a high-quality sample in data space (Ho et al., 2020; Song et al., 2020). This computational cost is especially problematic, and it restricts the practical deployment of diffusion models in real-time or resource-constrained settings (Salimans and Ho, 2022; Lu et al., 2022). Recent theoretical and empirical studies suggest that this inefficiency is closely related to a dynamical phase transition (bifurcation) that occurs during the reverse process (Raya and Ambrogioni, 2024; Biroli et al., 2024; Ambrogioni, 2025). In the early reverse steps, the trajectories stay near a stable fixed point whose distribution is close to the initial independent Gaussian, and little structure is present in the samples.