Iterative $α$-(de)Blending: a Minimalist Deterministic Diffusion Model (2305.03486v1)

Abstract: We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

• The paper introduces a simplified framework for deterministic denoising diffusion that redefines mappings between densities using iterative α-(de)blending.
• It leverages basic statistical operations and neural network deblending to achieve numerically stable results, surpassing DDIM in FID metrics on diverse datasets.
• The model’s inherent simplicity broadens its applicability for image generation, restoration, and other computer vision tasks, making diffusion modeling more accessible.

Overview of Iterative $\alpha$-(de)Blending: A Minimalist Deterministic Diffusion Model

The paper "Iterative $\alpha$-(de)Blending: A Minimalist Deterministic Diffusion Model" introduces a simplified deterministic diffusion model for generative modeling, called Iterative $\alpha$-(de)Blending (IADB). This model is designed to offer the advantages of deterministic denoising diffusion processes with reduced complexity. The authors postulate that the traditional diffusion models, which often require an understanding of advanced concepts such as Langevin dynamics and score matching, can be effectively simplified using basic statistical operations like blending and deblending densities.

Theoretical Foundations

At the core of the paper is the concept of mapping between two densities, achieved through an iterative process of blending and deblending samples. This mechanism transforms random paths between densities into deterministic mappings. The blending process linearly interpolates between samples from the two densities, namely $p_0$ and $p_1$. IADB then constructs trajectories that converge to deterministic mappings using neural networks trained for deblending operations.

Model Simplicity and Comparisons

IADB introduces a model that parallels the functionality of Denoising Diffusion Implicit Models (DDIMs) but with a fundamentally different derivation that relies on basic calculus and probability. This ensures that the model is simpler to implement, numerically stable, and capable of producing high-quality results. The paper posits that while DDIMs assume Gaussian noise, IADB extends this capability to arbitrary densities as long as they have finite variance.

Empirical Results

The authors validate IADB by demonstrating its performance in converting Gaussian noise into image data, such as cat or facial images. They note that on multiple datasets like LSUN Bedrooms, CelebA, and AFHQ Cats, IADB consistently outperforms DDIM in Fréchet Inception Distance (FID) metrics. The model's stability and numerical precision, especially in settings with fewer sampling steps, highlight its practical advancement over existing methodologies.

Broader Implications and Future Directions

IADB's inherent simplicity broadens accessibility to diffusion models for practitioners who might not be familiar with stochastic calculus or complex denoising frameworks. The implications of a more straightforward model extend to broader deployment possibilities in tasks like image generation, restoration, and even parameterization in computer graphics.

Future work could explore the integration of IADB with conditional setups, expanding its applicability in structured domain translations like image super-resolution, segmentation, or guided synthesis. Furthermore, enhancing the sampling procedure with advanced schedule tuning or leveraging the model's deterministic construction for real-time applications are potential avenues for extending this research.

Conclusion

Iterative $\alpha$-(de)Blending stands out as a minimalist yet effective approach to deterministic denoising diffusion, bridging conceptual simplicity with empirical excellence. The paper not only challenges the traditional derivations based on complex stochastic dynamics but also establishes a practical framework suitable for a wide range of density transformation tasks in computer vision and beyond.