Discrete diffusion is a promising framework for modeling and generating discrete data. In this work, we present Target Concrete Score Matching (TCSM), a novel and versatile objective for training and fine-tuning discrete diffusion models. TCSM provides a general framework with broad applicability. It supports pre-training discrete diffusion models directly from data samples, and many existing discrete diffusion approaches naturally emerge as special cases of our more general TCSM framework. Furthermore, the same TCSM objective extends to post-training of discrete diffusion models, including fine-tuning using reward functions or preference data, and distillation of knowledge from pre-trained autoregressive models. These new capabilities stem from the core idea of TCSM, estimating the concrete score of the target distribution, which resides in the original (clean) data space. This allows seamless integration with reward functions and pre-trained models, which inherently only operate in the clean data space rather than the noisy intermediate spaces of diffusion processes. Our experiments on language modeling tasks demonstrate that TCSM matches or surpasses current methods. Additionally, TCSM is versatile, applicable to both pre-training and post-training scenarios, offering greater flexibility and sample efficiency.
View on arXiv@article{zhang2025_2504.16431,
title={ Target Concrete Score Matching: A Holistic Framework for Discrete Diffusion },
author={ Ruixiang Zhang and Shuangfei Zhai and Yizhe Zhang and James Thornton and Zijing Ou and Joshua Susskind and Navdeep Jaitly },
journal={arXiv preprint arXiv:2504.16431},
year={ 2025 }
}