Discrete Copula Diffusion (2410.01949v2)

Abstract: Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just a few denoising steps, modern discrete diffusion models still require hundreds or even thousands of denoising steps to perform well. In this paper, we identify a fundamental limitation that prevents discrete diffusion models from achieving strong performance with fewer steps -- they fail to capture dependencies between output variables at each denoising step. To address this issue, we provide a formal explanation and introduce a general approach to supplement the missing dependency information by incorporating another deep generative model, termed the copula model. Our method does not require fine-tuning either the diffusion model or the copula model, yet it enables high-quality sample generation with significantly fewer denoising steps. When we apply this approach to autoregressive copula models, the combined model outperforms both models individually in unconditional and conditional text generation. Specifically, the hybrid model achieves better (un)conditional text generation using 8 to 32 times fewer denoising steps than the diffusion model alone. In addition to presenting an effective discrete diffusion generation algorithm, this paper emphasizes the importance of modeling inter-variable dependencies in discrete diffusion.

• The paper introduces a hybrid model that integrates copula techniques into discrete diffusion, significantly reducing the number of denoising steps required.
• It employs an I-projection method to combine univariate marginals from discrete diffusion with dependency data from autoregressive copula models.
• Empirical results show an 8–32x reduction in denoising steps, enhancing sample coherence and efficiency in text and sequence generation.

Analysis of Discrete Copula Diffusion: Enhancing Discrete Diffusion Models with Copula Models

Discrete diffusion models have demonstrated notable advances in modeling high-complexity data forms, including natural languages and DNA sequences. However, these models typically require extensive denoising steps—often hundreds or thousands—to generate high-quality samples. This contrasts with continuous diffusion models, which perform efficiently with fewer steps. The key challenge for discrete models is their inability to capture dependencies between variables in each denoising step.

Limitations in Existing Models

The fundamental limitation identified in discrete diffusion models arises from their assumption of variable independence during denoising steps. As a result, when multiple tokens are modified concurrently, the models fail to account for their joint probability. This results in incoherent sample generation, particularly when fewer denoising steps are used, as greater proportions of the sequence must be edited simultaneously.

Proposed Solution: Incorporating Copula Models

The paper proposes a solution that leverages another deep generative model, termed a copula model, to incorporate the missing dependency information. This approach involves integrating the copula model's ability to account for inter-variable dependencies during the discrete diffusion process at inference time. The combined model, referred to as Discrete Copula Diffusion (DCD), does not require fine-tuning and provides a framework where existing discrete diffusion models and copula models, such as autoregressive models, can be effectively combined.

Implementation and Impact

The DCD model achieves a significant reduction in the number of denoising steps needed to produce high-quality samples. Specifically, using this hybrid approach allows for 8 to 32 times fewer denoising steps compared to using a diffusion model alone, while maintaining or even improving the text generation quality. This advance has significant implications for the efficiency and scalability of discrete diffusion models.

Methodological Framework

1. Univariate Marginals and Copula Integration: The process begins with existing discrete diffusion models generating univariate marginals of the distribution. These marginals are then integrated with dependency information from an autoregressive copula model using an I-projection technique. This technique ensures that the combined distribution more accurately represents the true inter-variable dependencies without altering the learned diffusion and copula models.
2. Optimization Problem: The integration of the diffusion and copula models is framed as a convex optimization problem, where an efficient approximation of the combined distribution is solved, enhancing the approximation of the denoising distribution.
3. Autoregressive Application as Copula Models: Autoregressive models naturally encode dependencies between sequences. When combined with diffusion models, they enhance the generation process, ensuring coherent token prediction while leveraging conditioned data.

Empirical Validation and Results

The paper empirically validates the efficacy of the DCD approach across various tasks, including unconditional and conditional text generation, alongside protein sequence infilling. The results consistently demonstrate superior performance when comparing DCD against standalone diffusion or autoregressive models.

Implications and Future Directions

DCD sets a precedent for improving efficiency in discrete diffusion models, emphasizing the necessity of modeling inter-variable dependencies. The approach is particularly relevant for applications involving complex data structures where computational efficiency and sample quality are paramount. The research encourages further exploration into the theoretical frontiers of discrete diffusion modeling and the methodological innovations that can be achieved by integrating diverse modeling paradigms.

In conclusion, the Discrete Copula Diffusion model marks a significant advancement in discrete diffusion modeling, offering a versatile and effective solution for enhancing performance with reduced computational demands. This contributes robustly to the discourse on optimizing and deploying AI models in domains requiring high fidelity in large-scale sequence generation.