Understanding Diffusion Models: A Unified Perspective (2208.11970v1)

Abstract: Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

• The paper presents a unified ELBO derivation for diffusion models, emphasizing the balance between reconstruction fidelity and latent transition consistency.
• It demonstrates the equivalence between diffusion and score-based generative models, enabling effective score function learning across noise levels.
• It investigates guidance techniques like classifier-free and classifier guidance to enhance control and performance in conditional generation applications.

Understanding Diffusion Models: A Unified Perspective

The academic paper "Understanding Diffusion Models: A Unified Perspective" presents an insightful analysis of diffusion models, notably their interpretations, computational frameworks, and connections to related generative modeling techniques. The work focuses on constructing a comprehensive understanding of diffusion models through the lens of existing hierarchical variational models and score-based generative modeling.

Summary of Insights

Diffusion models are analyzed initially as a specific type of Markovian Hierarchical Variational Autoencoders (HVAEs). This approach differentiates diffusion models by enforcing restrictions on the encoder structure, specifically using linear Gaussian models, and maintaining the latent dimension equal to the data dimension. This framework preserves variance through a sequence of Gaussian transformations, leading to a latent distribution converging to Gaussian noise over successful time steps. These constraints not only facilitate tractable computation of the evidence lower bound (ELBO) but also simplify the optimization process.

Strategically, the paper emphasizes three important aspects of diffusion models:

1. ELBO Optimization: The work systematically derives the ELBO specific to diffusion models, highlighting its components such as the reconstruction term and the consistency term. Numerical results show that maximizing ELBO across latent transitions handles the correlations between latent transition consistency and reconstruction accuracy.
2. Equivalence to Score-Based Models: A core contribution is the bridging of diffusion models to score-based generative models, enabling a reinterpretation of the ELBO optimization process as learning score functions across noise levels. This perspective enhances the inherent flexibility of diffusion models by incorporating insights from energy-based modeling, circumventing the need for normalization through explicit score matching.
3. Guidance Techniques for Conditional Diffusion Models: The exploration of guidance methods such as Classifier Guidance and Classifier-Free Guidance provides methodologies for improving the integration of conditioning signals in diffusion models. This enhances control over conditional generation, proving essential in applications like text-conditioned image synthesis in DALL-E 2 and language-based tasks like Imagen.

Implications and Future Directions

The theoretical implications of this research revolve around the efficacy of employing infinite hierarchical structures in learning profound data representations, a concept emphasized through the smooth transition from Markovian HVAEs to continuous time stochastic processes. Moreover, leveraging score-based methods positions diffusion models as robust tools for generative tasks, validated by their successful application in contemporary state-of-the-art generative models.

Practically, a critical aspect lies in addressing the computational heaviness associated with large iterations required in sampling processes, a challenge that beckons further paper into optimizing denoising transitions and reducing computational overhead. Future research prospects could focus on refining conditional diffusion models to improve performance in multimodal data scenarios. Additionally, examining the potential to integrate interpretable latent structures within diffusion models could lead to new insights in unsupervised representation learning.

Conclusion

"Understanding Diffusion Models: A Unified Perspective" provides deep insights into the methodologies and theoretical underpinnings governing diffusion models, illustrating their robust potential and alignment with broader generative modeling strategies. As the field advances, these models are expected to play an increasingly pivotal role in solving complex generative challenges, underscoring the importance of the theoretical advancements and practical implications delineated in this paper.