Diffusion models as plug-and-play priors (2206.09012v3)

Abstract: We consider the problem of inferring high-dimensional data $\mathbf{x}$ in a model that consists of a prior $p(\mathbf{x})$ and an auxiliary differentiable constraint $c(\mathbf{x},\mathbf{y})$ on $x$ given some additional information $\mathbf{y}$. In this paper, the prior is an independently trained denoising diffusion generative model. The auxiliary constraint is expected to have a differentiable form, but can come from diverse sources. The possibility of such inference turns diffusion models into plug-and-play modules, thereby allowing a range of potential applications in adapting models to new domains and tasks, such as conditional generation or image segmentation. The structure of diffusion models allows us to perform approximate inference by iterating differentiation through the fixed denoising network enriched with different amounts of noise at each step. Considering many noised versions of $\mathbf{x}$ in evaluation of its fitness is a novel search mechanism that may lead to new algorithms for solving combinatorial optimization problems.

• The paper introduces the use of independently trained DDPMs as plug-and-play priors for conditionally constrained inference without retraining.
• It integrates differentiable constraints with the diffusion process to enable conditional image generation, semantic segmentation, and optimization.
• Empirical results demonstrate competitive performance, scalability, and transferability across various high-dimensional tasks.

Diffusion Models as Plug-and-Play Priors

The paper by Graikos et al. explores a novel application of denoising diffusion probabilistic models (DDPMs) as plug-and-play priors for various tasks, particularly within the context of learning complex distributions over high-dimensional continuous data. The central focus of the paper is utilizing independently trained DDPMs to perform inference tasks by integrating them with differentiable constraints, transforming these diffusion models into versatile modules that can adapt to a variety of domains and applications without requiring additional training of the model components.

Core Contributions and Methodology

The authors propose a method to use DDPMs as flexible priors that can be combined with differentiable constraints, enabling the inference of high-dimensional data that satisfy both the generative model's prior and external conditions. The approach is delineated through several key steps:

1. Problem Formulation: The primary problem involves inferring data constrained by a known condition, represented as a likelihood component or another form of differentiation-friendly function. The goal is to approximate the posterior of the form $p(x \mid y) \propto p(x) c(x, y)$, where $c(x, y)$ is the constraint depending on auxiliary data $y$.
2. Diffusion Models as Priors: The architecture leverages DDPMs as priors for inference problems, capitalizing on their robust capacity to capture detailed structures in data distribution. The diffusion prior is factored into ongoing steps of noise application followed by denoising, aligning the sample generation with the target constraint via iterative updates.
3. Plug-and-Play Inference without Retraining: Unlike traditional models requiring retraining or finetuning to blend priors with constraints, the proposed methodology advocates a plug-and-play adaptability where the diffusion models are used seamlessly without additional learning processes.
4. Applications in Conditional Generation: By combining the diffusion model with constraints derived from classifiers, the paper demonstrates conditional image generation capabilities. This involves generating images that satisfy certain class conditions and stylistic features simply by leveraging the diffusion process guided by classifiers' outputs.
5. Applications in Semantic Segmentation and Optimization: The method has been extended to include semantic segmentation tasks by treating DDPMs as latent guides for segmenting images without direct pixel-based inference, using the segmentation priors combined with external domain labels for domain adaptation tasks. Additionally, the structure enables potential optimization of combinatorial search problems, showcasing the flexibility of the approach in handling structured prediction tasks.

Results and Implications

The empirical evaluation demonstrates the versatility and potential of DDPMs as prior modules across different scopes:

• Numerical Performance: In the experiments, the application of DDPMs as plug-and-play priors delivered results comparable to state-of-the-art techniques across various tasks, including the Traveling Salesman Problem and image segmentation, displaying low rates of error and divergence from known ground-truth solutions.
• Scalability and Transferability: The proposed model exhibits advantageous scalability, operating effectively even in new contexts outside originally trained regions, enhancing its utility in real-world applications where domain transferability is critical.

Theoretical and Practical Implications

The research opens up important avenues in the context of generative modeling and inferential reasoning, wherein generative models like diffusion-based architectures can effectively serve multipurpose roles by functioning as integrative priors. This could impact future model architectures, leading to more generalized frameworks capable of seamless integration within various AI systems, reducing the computational overhead associated with model-specific retraining or adaptation procedures.

In summary, this paper contributes a valuable framework leveraging DDPMs for conditionally constrained inferences, enhancing the versatility of generative models and propelling innovations in image processing, structured data prediction, and optimization methods within artificial intelligence.