Understanding DDPM Latent Codes Through Optimal Transport (2202.07477v2)

Abstract: Diffusion models have recently outperformed alternative approaches to model the distribution of natural images, such as GANs. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space and an encoder map. While having important practical applications, such as estimation of the likelihood, the theoretical properties of this map are not yet fully understood. In the present work, we partially address this question for the popular case of the VP SDE (DDPM) approach. We show that, perhaps surprisingly, the DDPM encoder map coincides with the optimal transport map for common distributions; we support this claim theoretically and by extensive numerical experiments.

Overview of "Formatting Instructions for ICLR 2023 Conference Submissions"

The paper "Formatting Instructions for ICLR 2023 Conference Submissions" provides a comprehensive guide for authors in preparing their manuscripts for submission to the International Conference on Learning Representations (ICLR). The document is authored by Antiquus S. Hippocampus, Natalia Cerebro, Amelie P. Amygdale, Ji Q. Ren, Yevgeny LeNet, and other contributing researchers. It is an essential resource for authors aiming to align their submissions with the standard formatting guidelines required by the conference.

Formatting Guidelines

The document outlines detailed instructions specific to ICLR 2023 submissions. Authors are required to use the ICLR LaTeX style files, which are adaptations of the NeurIPS format. This ensures uniformity and facilitates efficient review processes. The formatting covers various aspects:

1. General Formatting Instructions: The main text should fit within a defined rectangle, with specific typeface and spacing requirements. The paper title, author names, and headings at different levels have distinct formatting styles to maintain consistency.
2. Headings Structure: A systematic hierarchy for headings is provided, including first-level, second-level, and third-level headings. Each level has precise spacing and alignment requirements.
3. Citations and References: The paper specifies the use of the natbib package for citation management, supporting both in-text citations and parenthetical references. Bibliographic entries follow a consistent style, facilitating clear attribution and academic rigor.
4. Figures and Tables: Authors must present figures and tables professionally, following designated captioning and placement conventions to ensure clarity and aesthetic appeal.

Notation and Style Conventions

The authors recommend a standardized notation to encourage consistency across different submissions. This includes suggested typographic representations for mathematical expressions, matrices, and graphs. While adherence to this notation is not compulsory, its use is encouraged for readability and uniformity.

Technical Considerations

The paper provides instructions for generating correctly formatted PostScript or PDF files tailored to US Letter specifications, opposing the A4 defaults seen elsewhere. Emphasis is placed on avoiding common LaTeX pitfalls, such as improper margin handling and manual figure positioning, advocating instead for the use of the graphicx package for robust figure inclusion.

Implications and Recommendations

The implications of adhering to these rigorous formatting guidelines are multifaceted. Practically, they facilitate seamless integration into conference proceedings, uphold production quality, and contribute to a cohesive presentation of research works. Theoretically, these norms support the dissemination of knowledge through structured and accessible documentation.

For future developments, the continual refinement of these guidelines could integrate evolving best practices in document preparation, accommodate new research presentation styles, or incorporate advancements in typographic technologies. This paper thus serves as both a current directive and a foundation for future iterations in academic paper formatting.

Overall, the "Formatting Instructions for ICLR 2023 Conference Submissions" acts as an indispensable reference for authors, ensuring that their submissions meet professional standards and contribute effectively to the academic dialogue at ICLR.