Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation (2303.00848v7)

Abstract: To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

• The paper shows that diffusion objectives can be interpreted as a weighted ELBO under monotonic weighting with Gaussian noise perturbation.
• It introduces new monotonic weightings that yield state-of-the-art FID and Inception scores on high-resolution ImageNet benchmarks.
• It proposes an adaptive noise scheduling strategy that minimizes loss estimation variance and enhances training efficiency.

Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation

The paper "Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation" offers a comprehensive analysis of diffusion models, focusing on the interplay between diffusion model objectives and the Evidence Lower Bound (ELBO). This research positions itself within a field that, although initially overshadowed, has recently gained significant traction due to its efficacy in high-quality generative tasks across multiple domains, including image, text, and speech.

Core Contributions

The paper elucidates that diffusion model objectives, although historically perceived as distinct from ELBO, inherently relate through a weighted integral of ELBOs across different noise levels. This integral depends on the specific diffusion objective's weighting. Notably, under the condition of monotonic weighting, the diffusion objectives align directly with the ELBO, augmented by Gaussian noise perturbation.

A systematic exploration and validation of these theoretical insights are provided through several new monotonic weightings. These weightings result in state-of-the-art FID scores on high-resolution benchmarks like ImageNet, underscoring their effectiveness.

Theoretical Insights

The paper introduces a unifying framework for understanding various diffusion model objectives as special instances of a weighted loss function. The weighting function plays a pivotal role, specifying the relative emphasis per noise level. Key findings include:

• Monotonic Weighting and ELBO: If the weighting function is monotonic, the diffusion objective equates to the ELBO with data augmentation, showing a significant overlap with methodologies that employ similar augmentation techniques.
• Loss Invariance: The authors describe the invariance of the weighted loss concerning the noise schedule, highlighting that only the endpoints matter for achieving efficient optimization.
• Adaptive Noise Scheduling: An adaptive noise schedule is proposed to minimize the variance of the loss estimator. This innovation aims to enhance optimization efficiency by dynamically adjusting the noise schedule during training.

Empirical Validation

The empirical section substantiates the theoretical claims by experimenting with various monotonic weightings on the ImageNet dataset. The findings are noteworthy, with proposed weightings delivering competitive or superior results compared to traditional approaches. The research demonstrated that these models achieved enhanced generative performance, as evidenced by improved FID and Inception scores on ImageNet at resolutions such as 64x64 and 128x128.

Implications and Future Directions

The implications of these findings are substantial, particularly in advancing our understanding of diffusion models' theoretical underpinnings. This research facilitates a direct comparison between diffusion models and other generative approaches under a unified theoretical framework. This equates the goals of optimizing data likelihood with state-of-the-art generative sampling quality.

Future work could delve into optimizing other generative models using these insights, potentially focusing on evaluating their performance against diffusion models under varied conditions. Another promising avenue involves extending these principles to non-generative settings, further exploring noise-induced augmentation's role in enhancing model robustness.

In conclusion, this paper bridges the theoretical gap between diffusion objectives and traditional ELBO methods, charting a path for more efficient and effective generative model training. By demystifying the role of noise as a data augmentation technique within diffusion models, it sets the stage for further research and application across AI domains.