Enhancing diffusion models with Gaussianization preprocessing
Abstract
Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory bifurcation, at which point substantial reconstruction begins. This issue degrades generation quality, especially in the early stages. Our primary objective is to mitigate bifurcation-related issues by preprocessing the training data to enhance reconstruction quality, particularly for small-scale network architectures. Specifically, we propose applying Gaussianization preprocessing to the training data to make the target distribution more closely resemble an independent Gaussian distribution, which serves as the initial density of the reconstruction process. This preprocessing step simplifies the model's task of learning the target distribution, thereby improving generation quality even in the early stages of reconstruction with small networks. The proposed method is, in principle, applicable to a broad range of generative tasks, enabling more stable and efficient sampling processes.
Summary
This paper addresses the slow sampling bottleneck in diffusion models, particularly the delay before trajectory bifurcation where significant reconstruction begins. This delay degrades generation quality, especially in early stages and with smaller networks. The authors propose a Gaussianization preprocessing step to mitigate this issue. This involves transforming the training data to more closely resemble an independent Gaussian distribution, which is the initial density of the reconstruction process. This simplification aims to ease the model's learning task, leading to improved generation quality and faster convergence. The method combines Independent Component Analysis (ICA) with one-dimensional Gaussianization of each component. ICA iteratively extracts independent components, and Gaussianization maps the marginal distributions to a standard Gaussian form. Diffusion models are then trained on this transformed data. During inference, samples are generated in the Gaussianized space and then mapped back to the original data space using the inverse transformation. The authors validate their approach on synthetic data generated from Gaussian Mixture Models (GMMs), comparing diffusion models trained on raw data versus Gaussianized data. The primary evaluation metric is the average log-likelihood, which quantifies the alignment between generated samples and the true data distribution. The results demonstrate faster convergence and improved stability during reconstruction with Gaussianization, especially for smaller network architectures.
Key Insights
- •Novel technique: The paper introduces a Gaussianization preprocessing method, combining ICA and KDE-based Gaussianization, to improve diffusion model efficiency. This differs from existing latent space methods (e.g., DiffuseVAE, LDMs) that rely on pre-trained autoencoders.
- •Faster convergence: The Gaussianized pipeline achieves high log-likelihood values within the first 20 reverse steps, whereas the baseline requires over 80 steps to reach similar performance, demonstrating significantly faster convergence.
- •Improved stability: Gaussianization leads to smoother, more stable reconstruction trajectories, avoiding the abrupt transitions associated with bifurcation instability in the baseline approach.
- •Network size independence: Gaussianization allows for high-quality reconstructions even with smaller network architectures (e.g., width 16), while the baseline relies on larger networks to achieve comparable results.
- •Training acceleration: Gaussianization preprocessing marginally accelerates the training process, leading to slightly faster reductions in training loss and convergence with fewer iterations.
- •Limitation: The method relies on ICA and KDE, which may face scalability challenges with high-dimensional data due to computational cost of these methods.
Practical Implications
- •Real-world applications: The improved efficiency and stability of diffusion models achieved through Gaussianization can benefit applications such as image generation, natural language processing, and video synthesis, especially in resource-constrained environments.
- •Beneficiaries: Researchers and engineers working on generative models, particularly diffusion models, can leverage this technique to improve the performance and efficiency of their models.
- •Implementation: Practitioners can implement Gaussianization preprocessing by integrating ICA and KDE-based Gaussianization into their existing diffusion model pipelines. The paper provides detailed steps for forward and inverse transformations.
- •Future research: Future research could focus on developing more efficient Gaussianization techniques for high-dimensional data, such as deep learning-based adaptive Gaussianization networks, and integrating Gaussianization with other advanced generative model techniques.