Optimizing Downstream Rewards in Pre-Trained Diffusion Models without Fine-Tuning or Differentiable Proxies

Core Concepts

A novel inference-time algorithm, SVDD, that optimizes downstream reward functions in pre-trained diffusion models without the need for fine-tuning or constructing differentiable proxy models.

Abstract

The paper proposes a new method, SVDD (Soft Value-based Decoding in Diffusion models), to optimize downstream reward functions in pre-trained diffusion models. The key ideas are:

Introducing soft value functions that predict how intermediate noisy states lead to high rewards in the future of the diffusion denoising process.
Presenting a new inference-time technique, SVDD, which obtains multiple noisy states from the policy (i.e., denoising map) of pre-trained diffusion models and selects the sample with the highest value function at each time step.

The SVDD approach has several advantages:

It does not require fine-tuning the generative model, unlike classifier-free guidance or RL-based fine-tuning methods.
It does not need to construct differentiable proxy models, unlike classifier guidance methods, allowing the use of non-differentiable reward feedback common in scientific domains.
It can be directly applied to recent discrete diffusion models without any modification.
The authors demonstrate the effectiveness of their methods across various domains, including image generation, molecule generation, and DNA/RNA generation.

Stats

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences.
Existing methods for optimizing downstream reward functions often require "differentiable" proxy models or involve computationally expensive fine-tuning of diffusion models.
The proposed SVDD-MC and SVDD-PM algorithms outperform baseline methods like Best-of-N and DPS across multiple domains.

Quotes

"Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely -generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces."
"Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way."

Key Insights Distilled From

Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding

by Xiner Li, Yu... at arxiv.org 09-12-2024

https://arxiv.org/pdf/2408.08252.pdf

Deeper Inquiries

How can the SVDD algorithm be extended to handle multi-objective optimization problems, where multiple reward functions need to be optimized simultaneously?

The SVDD algorithm can be extended to handle multi-objective optimization by incorporating a weighted sum or Pareto front approach to combine multiple reward functions into a single composite reward signal. In the context of SVDD, this could involve defining a new reward function ( r_{\text{multi}}(x) ) that aggregates the individual reward functions ( r_1(x), r_2(x), \ldots, r_n(x) ) as follows:
[
r_{\text{multi}}(x) = \sum_{i=1}^{n} w_i r_i(x)
]
where ( w_i ) are the weights assigned to each reward function, reflecting their relative importance in the optimization process. This composite reward can then be used in the SVDD framework to guide the sampling process.
Alternatively, a Pareto optimization approach could be employed, where the algorithm seeks to find a set of solutions that represent the best trade-offs among the multiple objectives. In this case, the soft value functions could be adapted to evaluate the trade-offs between different reward functions, allowing the SVDD algorithm to explore a diverse set of solutions that are optimal with respect to multiple criteria. This would enhance the algorithm's ability to generate designs that are not only high-performing in one aspect but also balanced across various objectives, thus broadening the applicability of SVDD in complex design spaces.

What are the potential limitations of the SVDD approach in terms of its ability to explore and discover novel designs that are significantly different from the pre-trained distribution?

One potential limitation of the SVDD approach is its inherent reliance on the pre-trained diffusion models, which are designed to capture the natural design space of the training data. As a result, the samples generated by SVDD are likely to remain close to the distribution of the training data, potentially limiting the exploration of novel designs that deviate significantly from this distribution. This proximity to the pre-trained model acts as a regularization mechanism, which, while beneficial for maintaining naturalness, may hinder the discovery of innovative or unconventional designs that could be valuable in applications such as drug discovery or creative content generation.
Additionally, the algorithm's performance is contingent upon the quality and diversity of the pre-trained model. If the pre-trained model lacks representation of certain design spaces or is biased towards specific types of solutions, the SVDD algorithm may struggle to generate diverse outputs. Furthermore, the optimization of reward functions that are learned from offline data can lead to overfitting, where the model becomes too specialized in optimizing for known rewards, further constraining its ability to explore uncharted territories in the design space.

Could the SVDD framework be adapted to work with other types of generative models beyond diffusion models, such as variational autoencoders or generative adversarial networks?

Yes, the SVDD framework could be adapted to work with other types of generative models, such as variational autoencoders (VAEs) or generative adversarial networks (GANs). The core principles of SVDD, which involve optimizing downstream reward functions without the need for fine-tuning or differentiable proxy models, can be applied to these generative architectures with some modifications.
For VAEs, the SVDD approach could leverage the latent space representation learned by the VAE to sample from a distribution that maximizes the expected reward. The soft value functions could be defined in the context of the VAE's latent space, guiding the sampling process to explore regions that yield high rewards while maintaining the generative model's ability to produce realistic samples.
In the case of GANs, the SVDD framework could be integrated into the generator's sampling process. The generator could produce multiple samples, and the soft value functions could evaluate these samples based on the reward feedback. The selection of samples could then be influenced by the value functions, similar to the SVDD approach, allowing for the generation of high-reward outputs while still adhering to the distribution learned by the GAN.
Overall, the adaptability of the SVDD framework to various generative models highlights its versatility and potential for broader applications in optimizing complex design problems across different domains.