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.

The fashion industry is one of the leading domains in the global e-commerce sector, prompting major online retailers to employ recommendation systems for product suggestions and customer convenience. While recommendation systems have been widely studied, most are designed for general e-commerce problems and struggle with the unique challenges of the fashion domain. To address these issues, we propose a sequential fashion recommendation framework that leverages a pre-trained large language model (LLM) enhanced with recommendation-specific prompts. Our framework employs parameter-efficient fine-tuning with extensive fashion data and introduces a novel mix-up-based retrieval technique for translating text into relevant product suggestions. Extensive experiments show our proposed framework significantly enhances fashion recommendation performance.