VDLM: Variable Diffusion LMs via Robust Latent-to-Text Rendering

Autoregressive language models decode left-to-right with irreversible commitments, limiting revision during multi-step reasoning. We propose \textbf{VDLM}, a modular variable diffusion language model that separates semantic planning from text rendering. VDLM applies LLaDA-style masked diffusion over semantic variable embeddings to enable iterative refinement in latent space, then post-trains the planner with trajectory-aware optimization using embedding-space rewards and values, avoiding text decoding inside the RL loop. To convert planned embeddings back to text, we use a \textbf{Vec2Text} renderer and introduce \textbf{embedding perturbations} to robustify decoding under planner noise. Across nine benchmarks spanning general reasoning, math, and code, VDLM is competitive in pre-training and yields substantial post-training improvements on long-form generation tasks, outperforming other baselines. These results highlight the effectiveness of embedding-space post-training and robust latent-to-text rendering for diffusion language modeling.