For order-d categorical Markov random fields, discrete-diffusion score learning plus tau-leaping attains end-to-end KL error of order (S^d + x)/n, replacing the unstructured S^D/n rate.
Discrete state diffusion models: A sample complexity perspective
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(\epsilon^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.
citation-role summary
background 1
citation-polarity summary
years
2026 4roles
background 1polarities
background 1representative citing papers
Under sparsity, discrete diffusion models with a regularized score estimator attain minimax-optimal KL divergence rates of order l log(eK^d/l)/n, adapting automatically to the unknown support size l.
Cola DLM proposes a hierarchical latent diffusion model that learns a text-to-latent mapping, fits a global semantic prior in continuous space with a block-causal DiT, and performs conditional decoding, establishing latent prior modeling as an alternative to token-level autoregressive language model
citing papers explorer
-
Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
For order-d categorical Markov random fields, discrete-diffusion score learning plus tau-leaping attains end-to-end KL error of order (S^d + x)/n, replacing the unstructured S^D/n rate.
-
Discrete Diffusion Models are Minimax Optimal Under Sparsity
Under sparsity, discrete diffusion models with a regularized score estimator attain minimax-optimal KL divergence rates of order l log(eK^d/l)/n, adapting automatically to the unknown support size l.
-
Continuous Latent Diffusion Language Model
Cola DLM proposes a hierarchical latent diffusion model that learns a text-to-latent mapping, fits a global semantic prior in continuous space with a block-causal DiT, and performs conditional decoding, establishing latent prior modeling as an alternative to token-level autoregressive language model
- Streamlining Analysis and Design of Two-Dimensional Electronic Spectroscopy using Machine Learning