Unlocking Guidance for Discrete State-Space Diffusion and Flow Models (2406.01572v4)

Abstract: Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has been realized using guidance on diffusion and flow models. However, these guidance approaches are not readily amenable to discrete state-space models. Consequently, we introduce a general and principled method for applying guidance on such models. Our method depends on leveraging continuous-time Markov processes on discrete state-spaces, which unlocks computational tractability for sampling from a desired guided distribution. We demonstrate the utility of our approach, Discrete Guidance, on a range of applications including guided generation of small-molecules, DNA sequences and protein sequences.

• The paper introduces a novel Discrete Guidance framework that uses CTMCs to perform efficient conditional sampling in discrete state-space models.
• It employs a first-order Taylor approximation to reduce computational complexity while preserving high sample quality.
• Empirical results show improved control and performance across image, molecule, DNA, and protein generation tasks.

An Expert Perspective on "Unlocking Guidance for Discrete State-Space Diffusion and Flow Models"

Overview

The paper "Unlocking Guidance for Discrete State-Space Diffusion and Flow Models" addresses a significant gap in the generative modeling of discrete state-spaces. While existing methods for continuous state-spaces allow for guided sample generation, these approaches are not readily extendable to discrete state-spaces. The authors present a novel method called Discrete Guidance (DG) to apply guidance in discrete state-space diffusion and flow models, leveraging continuous-time Markov processes (CTMCs).

Key Contributions

1. Discrete Guidance Framework:
   • The authors introduce a principled framework for performing guidance on discrete state-spaces via CTMCs. This involves reformulating the guidance problem to be tractable, which is non-trivial given the combinatorial complexity inherent in discrete state spaces.
   • They derive the conditional rates necessary for guided regeneration using Bayes' theorem, facilitating both predictor guidance (PG) and predictor-free guidance (PFG).
2. Computational Efficiency:
   • Recognizing the computational challenges, the paper proposes a first-order Taylor series approximation, termed Taylor-approximated guidance (TAG), to make sampling more efficient without significant loss in sample quality.
3. Empirical Validation:
   • The utility of Discrete Guidance is demonstrated across various domains including image generation, small molecule design, DNA sequence generation, and protein sequence generation.
   • For each domain, the authors validate their approach by addressing specific conditional generation tasks and showing that DG improves sample quality and aligns with the desired properties.

Methodological Insights

The authors leverage CTMCs to design a tractable guidance mechanism for discrete state-space models. The discrete versions of diffusion and flow models depend on rate matrices that dictate transition probabilities between states. By incorporating guidance, these matrices are modulated based on a predictive distribution, allowing samples to meet desired properties efficiently.

The paper also addresses the problem of high computational cost in exact calculations by deploying the Taylor-approximated guidance technique. This reduces the burden from $\mathcal{O}(D \times S)$ to $\mathcal{O}(1)$ complexity for each sampling step, making the approach feasible for large, real-world applications.

Empirical Demonstrations

1. Image Modeling:
   • Guided conditional CIFAR-10 image generation demonstrated that Discrete Guidance with the Taylor-approximated approach could achieve higher Inception Scores and lower Fréchet Inception Distances compared to unguided models.
   • This suggests that DG helps to produce more recognizable and diverse images.
2. Small Molecules:
   • The authors used DG in generating molecules with specified numbers of rings and lipophilicity values. Results indicated a high degree of control over the generated properties, reflecting the efficacy of the guidance mechanism.
   • This has practical importance for drug discovery and chemical synthesis where specific molecular properties are often desired.
3. DNA Sequence Design:
   • For enhancing the cell-type specificity of DNA sequences, Discrete Guidance outperformed other methods like Dirichlet Flow Matching (DirFM) in both classifier-guided and classifier-free settings.
   • This demonstrates DG's potential for applications like synthetic biology where precise control of DNA sequences can drive functional outcomes.
4. Protein Stability:
   • The authors showed how guiding inverse-folding models with a stability predictor improves the generated sequences' structural stability without sacrificing their ability to fold correctly.
   • This is significant for protein engineering, where stability is a crucial parameter for therapeutic and industrial applications.

Discussion and Implications

The methodological contributions of this paper have far-reaching implications. By enabling effective guidance in discrete state-space generative models, the proposed Discrete Guidance framework expands the toolkit available for various scientific domains. This can drive advancements in areas like materials science, synthetic biology, and drug discovery, where controlled generation of discrete entities is crucial.

Additionally, the empirical results underline the broad applicability and effectiveness of Discrete Guidance. Future directions may include exploring DG in other domains such as text generation with LLMs and extending the theoretical framework to integrate more complex forms of guidance and interpretability.

In conclusion, this paper presents a comprehensive and technically robust approach to bringing the benefits of guidance to discrete state-space generative models. The combination of theoretical groundwork with practical efficiency paves the way for significant advancements in generative modeling applications.