LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language
  Diffusion Models
Authors: name: Fengqi Zhu, name: Rongzhen Wang, name: Shen Nie, name: Xiaolu Zhang, name: Chunwei Wu, name: Jun Hu, name: Jun Zhou, name: Jianfei Chen, name: Yankai Lin, name: Ji-Rong Wen, name: Chongxuan Li

While Masked Diffusion Models (MDMs), such as LLaDA, present a promising
paradigm for language modeling, there has been relatively little effort in
aligning these models with human preferences via reinforcement learning. The
challenge primarily arises from the high variance in Evidence Lower Bound
(ELBO)-based likelihood estimates required for preference optimization. To
address this issue, we propose Variance-Reduced Preference Optimization (VRPO),
a framework that formally analyzes the variance of ELBO estimators and derives
bounds on both the bias and variance of preference optimization gradients.
Building on this theoretical foundation, we introduce unbiased variance
reduction strategies, including optimal Monte Carlo budget allocation and
antithetic sampling, that significantly improve the performance of MDM
alignment. We demonstrate the effectiveness of VRPO by applying it to LLaDA,
and the resulting model, LLaDA 1.5, outperforms its SFT-only predecessor
consistently and significantly across mathematical (GSM8K +4.7), code
(HumanEval +3.0, MBPP +1.8), and alignment benchmarks (IFEval +4.0, Arena-Hard
+4.3). Furthermore, LLaDA 1.5 demonstrates a highly competitive mathematical
performance compared to strong language MDMs and ARMs. Project page:
https://ml-gsai.github.io/LLaDA-1.5-Demo/.