Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise (2208.09392v1)

Abstract: Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the choice of image degradation, and in fact an entire family of generative models can be constructed by varying this choice. Even when using completely deterministic degradations (e.g., blur, masking, and more), the training and test-time update rules that underlie diffusion models can be easily generalized to create generative models. The success of these fully deterministic models calls into question the community's understanding of diffusion models, which relies on noise in either gradient Langevin dynamics or variational inference, and paves the way for generalized diffusion models that invert arbitrary processes. Our code is available at https://github.com/arpitbansal297/Cold-Diffusion-Models

• The paper introduces a deterministic framework that replaces Gaussian noise with targeted image transformations such as blurring, masking, and downsampling.
• The paper presents an innovative sampling algorithm that robustly reconstructs images and shows competitive performance on standard metrics like FID scores.
• The empirical validation across deblurring, inpainting, and super-resolution tasks underscores the method's practical benefits in image restoration and generation.

Overview of "Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise"

This paper introduces a novel concept in the field of diffusion models, termed "Cold Diffusion," which demonstrates that the reliance on Gaussian noise for image generation and restoration is not a strict necessity. The authors propose that deterministic transformations can be effectively utilized in diffusion models, challenging established paradigms and potentially expanding the scope of generative modeling.

Key Contributions

The paper articulates the development of generalized diffusion models capable of inverting deterministic image transformations such as blurring, masking, and downsampling. This departure from traditional noise-based methods offers a fresh perspective on how generative behavior can be elicited from diffusion models.

1. Model Generalization: By replacing random Gaussian noise with deterministic operations, the authors present a framework where conventional diffusion models can be extended to handle a broader spectrum of image degradations. This approach essentially redefines the architectural needs of generative models and questions the dependency on stochastic processes.
2. Algorithmic Innovation: The authors propose an improved sampling algorithm—distinct from traditional Langevin dynamics-based methods—that is particularly well-suited for reconstructing images subjected to deterministic transformations. This algorithm exhibits robustness to restoration errors, which is critical for achieving high-quality generative outcomes.
3. Empirical Validation: Demonstrations across standard tasks such as deblurring, inpainting, super-resolution, and even unconventional transformations like snowification underscore the practical effectiveness of cold diffusion models. The models are evaluated using FID scores and related metrics, showing competitive performance.

Theoretical Insights

Cold diffusion models suggest that the theoretical foundations of diffusion as a random walk guided by Gaussian noise can be revisited. The authors emphasize that deterministic paths through image space can yield similar or even superior generative results when appropriately designed. This raises intriguing questions about the potential for non-noise-based methods in other classes of generative models.

Implications and Future Directions

By successfully removing the dependency on stochastic noise, the methodological advancements outlined in the paper pave the way for the exploration of various deterministic transformations that could confer distinct advantages in speed, accuracy, and interpretability.

• Practical Applications: Especially in fields like image restoration, where specific deterministic effects are prevalent (e.g., blurring), adopting cold diffusion could lead to more efficient restoration methods.
• Theoretical Exploration: Theoretically, this work could inspire research into understanding the boundaries of diffusion models and where deterministic transformations might offer complementary strengths to noise-based methods.
• Generative Capabilities: In generative tasks, cold diffusion could be leveraged alongside or in place of GANs, especially in contexts where noise might obscure important features or where deterministic transformations are more representative of the real-world degradations.

Conclusion

The introduction of cold diffusion marks a noteworthy shift in the understanding and application of diffusion models. It calls for a reconsideration of foundational assumptions in generative modeling, especially concerning the necessity of noise. This paper sets a precedent for diversifying the toolkit available to researchers and practitioners in the AI and image processing communities and signals a promising direction for future innovations in both theory and application.