Discrete Diffusion with Sample-Efficient Estimators for Conditionals
arXiv:2602.20293v1 Announce Type: new Abstract: We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than approximating a discrete analog of a score function, our formulation treats single-site conditional probabilities as the fundamental objects that parameterize the reverse diffusion process. We employ a sample-efficient method known as Neural Interaction Screening Estimator (NeurISE) to estimate these conditionals in the diffusion dynamics. Controlled experiments on synthetic Ising models, MNIST, and scientific data sets produced by a D-Wave quantum annealer, synthetic Potts model and one-dimensional quantum systems demonstrate the proposed approach. On the binary data sets, these experiments demonstrate that the proposed approach outperforms popular existing methods including ratio-based approaches, achievi
arXiv:2602.20293v1 Announce Type: new Abstract: We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than approximating a discrete analog of a score function, our formulation treats single-site conditional probabilities as the fundamental objects that parameterize the reverse diffusion process. We employ a sample-efficient method known as Neural Interaction Screening Estimator (NeurISE) to estimate these conditionals in the diffusion dynamics. Controlled experiments on synthetic Ising models, MNIST, and scientific data sets produced by a D-Wave quantum annealer, synthetic Potts model and one-dimensional quantum systems demonstrate the proposed approach. On the binary data sets, these experiments demonstrate that the proposed approach outperforms popular existing methods including ratio-based approaches, achieving improved performance in total variation, cross-correlations, and kernel density estimation metrics.
Executive Summary
This study introduces a discrete denoising diffusion framework that utilizes a sample-efficient estimator, NeurISE, to estimate single-site conditionals in the reverse diffusion process. By treating single-site conditional probabilities as fundamental objects, the proposed approach outperforms existing methods, including ratio-based approaches, in terms of total variation, cross-correlations, and kernel density estimation metrics. Controlled experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed approach, particularly on binary data sets. This research contributes to the development of efficient generative modeling techniques for discrete state spaces and has implications for various applications, including machine learning, quantum computing, and scientific data analysis.
Key Points
- ▸ The proposed discrete denoising diffusion framework integrates NeurISE to estimate single-site conditionals.
- ▸ The approach treats single-site conditional probabilities as fundamental objects in the reverse diffusion process.
- ▸ Controlled experiments demonstrate improved performance compared to existing methods, including ratio-based approaches.
Merits
Theoretical Foundation
The proposed framework is grounded in a sound theoretical foundation, treating single-site conditional probabilities as fundamental objects in the reverse diffusion process, which provides a clear and coherent formulation of the discrete denoising diffusion process.
Empirical Validity
The controlled experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed approach, providing empirical evidence for its validity and reliability.
Demerits
Computational Complexity
The use of NeurISE, a sample-efficient estimator, may lead to increased computational complexity, particularly for large-scale datasets, which could limit the practical applicability of the proposed approach.
Scalability
The scalability of the proposed approach, particularly for high-dimensional datasets, remains a topic of investigation, and further research is needed to fully realize its potential in practical applications.
Expert Commentary
The proposed discrete denoising diffusion framework is a significant contribution to the development of efficient generative modeling techniques for discrete state spaces. By treating single-site conditional probabilities as fundamental objects, the approach provides a clear and coherent formulation of the discrete denoising diffusion process. The use of NeurISE, a sample-efficient estimator, is a key innovation that enables the proposed approach to outperform existing methods. However, the computational complexity and scalability of the proposed approach remain topics of investigation, and further research is needed to fully realize its potential in practical applications. Overall, this research has the potential to impact various fields, including machine learning, quantum computing, and scientific data analysis.
Recommendations
- ✓ Future research should focus on exploring the scalability of the proposed approach for high-dimensional datasets and investigating its applicability to other machine learning tasks.
- ✓ The proposed approach should be further developed and refined to address the limitations of computational complexity and scalability.
