Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models

Abstract: In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost that is orthogonal to sampling time. We tackle the question of how to improve diversity and sample efficiency by moving beyond the common assumption of independent samples. We propose particle guidance, an extension of diffusion-based generative sampling where a joint-particle time-evolving potential enforces diversity. We analyze theoretically the joint distribution that particle guidance generates, how to learn a potential that achieves optimal diversity, and the connections with methods in other disciplines. Empirically, we test the framework both in the setting of conditional image generation, where we are able to increase diversity without affecting quality, and molecular conformer generation, where we reduce the state-of-the-art median error by 13% on average.

• The paper presents Particle Guidance, a technique that integrates a joint-particle potential into reverse diffusion to boost sample diversity.
• It offers a rigorous theoretical analysis connecting the joint potential to optimal diversity, drawing insights from molecular simulations and enhanced sampling methods.
• Empirical demonstrations in text-to-image and molecular conformer generation reveal significant improvements in output diversity and reduced median errors.

Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models

The paper presents an innovative approach to enhance the diversity and efficiency of sample generation in diffusion models—termed "Particle Guidance" (PG). This technique advances past the common independence assumptions of generative samples, aiming to optimize diversity by introducing dependencies among them.

Key Contributions

The authors introduce a theoretically motivated framework extending diffusion-based generative sampling called particle guidance. This framework uses a joint potential across the sampling process to enforce diversity, thereby improving sample efficiency. Key contributions in the paper include:

1. Framework Definition: Introducing the concept of particle guidance, which incorporates a joint-particle time-evolving potential in reverse diffusion processes for enhanced sample diversity.
2. Theoretical Analysis: Providing analytic expressions for the joint potential that can achieve optimal diversity and analyzing its connection to other disciplines such as molecular simulations and enhanced sampling techniques.
3. Empirical Demonstration: Validating particle guidance in both conditional image generation and molecular conformer generation, showing significant improvements. For instance, the method increased the diversity in the text-to-image generation and reduced median errors in molecular conformer generation.

Theoretical Framework

The paper presents a sophisticated view of how diffusion models can be extended for sampling processes. Traditional models like Stein Variational Gradient Descent are leveraged, but they face limitations in efficiently sampling complex distributions like images. Particle Guidance tackles these challenges, aiming for diversity without compromising the quality or increasing the sampling time of traditional generative models.

The joint distribution generated through particle guidance allows for the integration of additional forces such as electrostatic interactions, highlighting its utility in physically-motivated systems. The model handles time-evolving potentials in a manner that respects the underlying data distribution while moving towards a desired representation, thus offering a form of controlled sampling diversity.

Applications and Results

The empirical evaluation exhibits the potential of particle guidance in real-world applications:

• Text-to-Image Generation: Particle guidance improved the diversity metrics in Stable Diffusion outputs, maintaining visual quality while reducing mode collapse. The method was tested on a popular data set where it showcased improvements in visual distinctness over traditional I.I.D. sampling.
• Molecular Conformer Generation: The model outperforms current state-of-the-art methods in precision and coverage for conformer generation. Specifically, particle guidance reduced the median error versus previous models, evidencing enhanced sample spread across the distribution.

Implications and Future Work

The proposed particle guidance framework opens new pathways for sampling diverse sets efficiently. The potential applications extend beyond image generation and computational chemistry, touching AI's broader contact points with simulation disciplines. This approach may fundamentally redefining generative model efficiencies across diverse computational spectrums.

Moving forward, exploring adaptive potentials in real-time inference offers promising avenues. Additionally, theoretical exploration into the implications of modified marginal distributions by such sampling frameworks poses significant interest. The blend of machine learning with physically inspired constraints or objectives also hints at new intersections ripe for exploration.

The paper represents an integration effort across finely-grained computational methodologies and state-the-art generative techniques. While producing meaningful strides in balancing diversity and fidelity, it lays firm groundwork for deeper investigations into sample dependency generation.