GUD: Generation with Unified Diffusion (2410.02667v1)

Abstract: Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we revisit diffusion models by exploring three key design aspects: 1) the choice of representation in which the diffusion process operates (e.g. pixel-, PCA-, Fourier-, or wavelet-basis), 2) the prior distribution that data is transformed into during diffusion (e.g. Gaussian with covariance $\Sigma$), and 3) the scheduling of noise levels applied separately to different parts of the data, captured by a component-wise noise schedule. Incorporating the flexibility in these choices, we develop a unified framework for diffusion generative models with greatly enhanced design freedom. In particular, we introduce soft-conditioning models that smoothly interpolate between standard diffusion models and autoregressive models (in any basis), conceptually bridging these two approaches. Our framework opens up a wide design space which may lead to more efficient training and data generation, and paves the way to novel architectures integrating different generative approaches and generation tasks.

• The paper introduces GUD, a unified diffusion framework that leverages flexible bases, adaptive priors, and noise schedules to boost generative performance.
• It demonstrates that component-wise noise scheduling effectively interpolates between diffusion and autoregressive models for enhanced output quality.
• The framework bridges diffusive and autoregressive techniques, offering new pathways for efficient training and versatile generative applications.

Overview of "GUD: Generation with Unified Diffusion"

"Generation with Unified Diffusion" (GUD) introduces an innovative framework for diffusion-based generative models, expanding the design space and flexibility of existing approaches by integrating concepts from both physics and machine learning. It reexamines diffusion models through three primary dimensions: the basis in which diffusion occurs, the prior distribution to which data is transformed, and the scheduling of noise levels across individual data components.

Key Aspects of the Framework

1. Choice of Basis: GUD offers the freedom to choose the basis of operation (e.g., pixel, PCA, Fourier, wavelet) in which the diffusion process is diagonalizable. This allows tailored representations that can potentially enhance model efficiency and performance by selecting the most suitable data basis.
2. Prior Distribution: The framework allows flexibility in modeling the prior distribution that the data approaches during diffusion. This includes options like Gaussian distributions with varying covariances, enabling different statistical properties in the generated noise.
3. Component-Wise Noise Schedule: GUD introduces a component-specific noise schedule, which provides nuanced control over how noise is added during the diffusion process. This element of design permits interpolation between standard diffusion and autoregressive models, facilitating a spectrum of generation processes where each component can have its own tailored schedule.

Implications and Experimental Findings

The paper explores the impact of these new design variables through various experimental procedures. Notably:

• Soft-Conditioning: By adjusting the noise schedules, GUD demonstrates its ability to transition between diffusive and autoregressive generations. Experiments conducted on real-world datasets illustrate that altering these schedules can drastically affect the model's generative quality and operational dynamics.
• Design Flexibility and Application Possibilities: The unification of diffusion with autoregressive approaches opens possibilities for efficient model training and potential applications in tasks like image extension, considering GUD's capacity to condition on pre-generated information dynamically.
• Future Optimizations: The results suggest significant untapped potential to adopt and refine these new parameters for optimizing generative performance. Future work is encouraged to investigate methods for efficiently navigating this expanded design space to enhance model capabilities further.

Theoretical and Practical Contributions

The introduction of the GUD framework offers both a theoretical expansion and practical advance for generative models:

• Integration of Diffusive and Autoregressive Models: This unified framework helps bridge the gap between distinct generative approaches, allowing a seamless transition with soft-conditioning capabilities.
• Incorporation of Renormalization Group Concepts: By drawing parallels to RG flows from physics, the paper provides a fresh perspective on information erasure in generative models, potentially leading to novel theoretical insights and computational strategies.
• Robustness across Generative Tasks: The demonstrated capacity for handling varied generative tasks, including multi-scale and sequential tasks, suggests a robust applicability of GUD across domains requiring complex data generation processes.

In summary, the GUD framework stands as a significant contribution to the evolution of generative modeling, providing a versatile and comprehensive architecture poised to enhance the efficacy of diffusion-based methods and inspire future advancements in the field of artificial intelligence.