Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models

• URL: http://arxiv.org/abs/2604.16565v2
• Date: Thu, 23 Apr 2026 12:41:25 GMT
• Title: Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models
• Abstract summary: Bidirectional Manifold Consistency (BMC) is a training-free, unsupervised metric.<n>BMC serves as a robust discriminator of solution validity without ground truth answer.<n>Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.
• Score: 30.607422839762553
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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