Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo (2502.12786v1)

Abstract: Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.

• The paper presents an innovative distillation technique for energy-based diffusion models that stabilizes training through a Helmholtz-inspired loss function.
• It demonstrates improved generative performance with lower FID scores on benchmarks such as CIFAR-10 and CelebA.
• The integration of Sequential Monte Carlo enables controllable and compositional sampling, offering dynamic thresholding for bounded generation.

Overview of Distilled Energy Diffusion Models and Sequential Monte Carlo

The paper "Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo" introduces a novel framework for enhancing the training and sampling procedures of energy-parameterized diffusion models. This work addresses existing challenges in the field by proposing a more stable and efficient approach to model training through energy function distillation, in conjunction with the benefits of sequential Monte Carlo (SMC).

Diffusion models have established their dominance within generative modeling due to their strong performance across various domains. However, they still encounter issues such as slow training speeds, conditioning effectiveness, and challenges in composing different model instances. This paper identifies that these limitations partially arise from the instability of training energy-parameterized diffusion models, where architectural constraints and the need for multiple gradient computations exacerbate their training difficulties.

Main Contributions

1. Distillation Technique for Energy-Based Models: The authors present an innovative training method to distill scores from pretrained diffusion models into energy-based models. They develop a loss function akin to a Helmholtz decomposition, facilitating learning a conservative component of the score field. This allows the modeled energy to lend itself efficiently to lower variance losses and, thus, more stable training compared to traditional denoising score-matching (DSM).
2. Performance Metrics: The paper demonstrates improved generative performance over prior energy-parameterized models, as measured by lower Frechet Inception Distance (FID) scores across datasets such as CIFAR-10 and CelebA. This improvement signals the model's ability to generate samples more closely aligned with the true data distribution.
3. Feynman Kac Model and SMC Integration: By casting the sampling procedure into a Feynman Kac model, this work enables controllable composition and generation. Potentials derived from the learned energy functions guide the sampling process, allowing for temperature-controlled sampling and composition of models through SMC.
4. Application in Compositional and Bounded Generation: The integration of SMC allows not only for composition of diffusion models to synthesize new distributions but also for applying constraints and employing dynamic thresholding to control generation within specified boundaries.

Implications and Future Developments

Practically, this research suggests that energy-parameterized models can be made more computationally efficient and robust against previously noted instabilities. On a theoretical level, this work expands the applicability of diffusion models by incorporating the advantages of energy-based training methods and SMC. In terms of future prospects, this work lays the groundwork for advanced methodologies in AI-driven compositions and restrictions by offering a template for structuring and modulating samples with nuanced control.

Furthermore, the implications of such control mechanisms are far-reaching, extending possibilities in various modalities such as natural language processing and complex control systems, where precision and adaptability are paramount. The alignment with ongoing developments in optimal transport further underscores the potential utility in refined generative processes, weighing heavily on the accurate reproduction of data distributions.

The methodologies and findings presented in this paper hold promise for refining and extending existing AI frameworks, allowing for more dynamic, efficient, and capable generative models spanning various fields of application.