Diffusion Language Models (DLMs) offer order-agnostic generation that can explore many possible decoding trajectories. However, current decoding methods commit to a single trajectory, limiting exploration in trajectory space. We introduce Order-Token Search to explore this space through jointly searching over generation order and token values. Its core is a likelihood estimator that scores denoising actions, enabling stable pruning and efficient exploration of diverse trajectories. Across mathematical reasoning and coding benchmarks, Order-Token Search consistently outperforms baselines on GSM8K, MATH500, Countdown, and HumanEval (3.1%, 3.8%, 7.9%, and 6.8% absolute over backbone), reaching accuracy comparable to diffu-GRPO post-training. Our work establishes joint search as a key component for advancing decoding in DLMs.

In the constant updates of the product dialogue systems, we need to retrain the natural language understanding (NLU) model as new data from the real users would be merged into the existing data accumulated in the last updates. Within the newly added data, new intents would emerge and might have semantic entanglement with the existing intents, e.g. new intents that are semantically too specific or generic are actually a subset or superset of some existing intents in the semantic space, thus impairing the robustness of the NLU model.As the first attempt to solve this problem, we setup a new benchmark consisting of 4 Dialogue Version Control dataSets (DialogVCS). We formulate the intent detection with imperfect data in the system update as a multi-label classification task with positive but unlabeled intents, which asks the models to recognize all the proper intents, including the ones with semantic entanglement, in the inference.We also propose comprehensive baseline models and conduct in-depth analyses for the benchmark, showing that the semantically entangled intents can be effectively recognized with an automatic workflow. Our code and dataset are available at https://github.com/Zefan-Cai/DialogVCS.

Handwritten mathematical expression recognition (HMER) is a multidisciplinary task that generates LaTeX sequences from images. Existing approaches, employing tree decoders within attention-based encoder-decoder architectures, aim to capture the hierarchical tree structure, but are limited by CFGs and pre-generated triplet data, hindering expandability and neglecting visual ambiguity challenges. This article investigates the distinctive language characteristics of LaTeX mathematical expressions, revealing two key observations: 1) the presence of explicit structural symbols, and 2) the treatment of symbols, particularly letters, as minimal units with context-dependent semantics, representing variables or constants. Rooted in these properties, we propose that language models have the potential to synchronously and complementarily provide both structural and semantic information, making them suitable for correction of HMER. To validate our proposition, we propose an architecture called Recognize and Language Fusion Network (RLFN), which integrates recognition and language features to output corrected sequences while jointly optimizing with a string decoder recognition model. Experiments show that RLFN outperforms existing state-of-the-art methods on the CROHME 2014/2016/2019 datasets.