A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) is the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation during training. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, they incur significant memory overhead due to the need to retain all MC samples for the gradient computation of non-linear terms in the RL objective, and thus restrict feasible sample sizes, leading to imprecise likelihood approximations and distorted RL objective. To address this, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, improving likelihood approximations and RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

Recently, large reasoning models have achieved impressive performance on various tasks by employing human-like deep thinking. However, the lengthy thinking process substantially increases inference overhead, making efficiency a critical bottleneck. In this work, we first demonstrate that NoThinking, which prompts the reasoning model to skip thinking and directly generate the final solution, is a better choice for relatively simple tasks in terms of both performance and efficiency. Motivated by this, we propose AdaptThink, a novel RL algorithm to teach reasoning models to choose the optimal thinking mode adaptively based on problem difficulty. Specifically, AdaptThink features two core components: (1) a constrained optimization objective that encourages the model to choose NoThinking while maintaining the overall performance; (2) an importance sampling strategy that balances Thinking and NoThinking samples during on-policy training, thereby enabling cold start and allowing the model to explore and exploit both thinking modes throughout the training process. Our experiments indicate that AdaptThink significantly reduces the inference costs while further enhancing performance. Notably, on three math datasets, AdaptThink reduces the average response length of DeepSeek-R1-Distill-Qwen-1.5B by 53% and improves its accuracy by 2.4%, highlighting the promise of adaptive thinking-mode selection for optimizing the balance between reasoning quality and efficiency.