Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models
For researchers working with diffusion language models, this work provides a practical, unsupervised method to verify reasoning quality, addressing a key bottleneck in deploying these models for complex tasks.
The paper proposes Bidirectional Manifold Consistency (BMC), a training-free metric that uses geometric stability to verify reasoning traces in diffusion language models. BMC effectively discriminates valid from invalid solutions without ground truth, improves inference via rejection resampling, and serves as a dense reward for alignment, outperforming standard baselines.
While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.