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

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes Bidirectional Manifold Consistency (BMC), a training-free forward-mask/backward-reconstruct stability score for dLLMs, used for error diagnosis, rejection resampling (MGRS), and as a dense RL reward.

Problem

Verifying whether diffusion LLMs reach correct answers via valid reasoning traces without ground truth or external verifiers.

Approach

Scores a generated dLLM output by masking a portion of it, reconstructing with a few denoising steps, and measuring similarity between original and reconstruction (token, semantic, number, answer, char, confidence composite); the stability is interpreted as manifold attraction and used as a verifier, resampling criterion, and gated dense reward.

Key results

• On GSM8K with Dream-7B, BMC reaches 0.898 AUROC for error diagnosis versus 0.641 for Model Confidence and 0.684 for Self-Consistency.
• MGRS with LLaDA improves GSM8K accuracy to 79.5% versus 70.5% for standard sampling at N=3 budget with sample efficiency 3.98.
• Geometric Alignment with LLaDA reaches 41.6% on MATH at 512 tokens, +4.4 over Outcome RL, per the paper's table.

Surprising findings

• Confidence-based Best-of-N degrades MATH accuracy with LLaDA (negative sample efficiency), indicating token probability is a poor validity proxy.
• Cross-Entropy component of the BMC score lowers composite AUROC (0.821 to 0.794) and is excluded.

Limitations

• Composite score uses hand-chosen or task-optimized weights; optimized weights are tuned on the evaluation task.
• Several theoretical propositions are proof sketches and the paper itself notes they are motivating rather than strict guarantees.
• Semantic similarity can collapse on numeric changes, requiring complementary metrics.

Experimental setup

Datasets: GSM8K MATH ARC-Challenge GPQA

Benchmarks: GSM8K MATH ARC-C GPQA

Metrics: AUROC AUPR Accuracy Sample Efficiency

Baselines: Model Confidence Self-Consistency Self-Evaluation Standard Sampling Best-of-N SFT Outcome RL

Builds on: Sandwiched Policy Gradient d1 TraceRL GRPO

Closest papers by meaning

• Break the Block: Dynamic-size Reasoning Blocks for Diffusion Large Language Models via Monotonic Entropy Descent with Reinforcement Learning (ICML 2026 · similarity 0.87)
• The Flexibility Trap: Rethinking the Value of Arbitrary Order in Diffusion Language Models (ICML 2026 · similarity 0.87)
• On the Reasoning Abilities of Masked Diffusion Language Models (ICLR 2026 · similarity 0.87)
• d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning (NeurIPS 2025 · similarity 0.87)
• Efficient Test-Time Scaling via Hierarchical Search and Self-Verification for Discrete Diffusion Language Models (ICML 2026 · similarity 0.87)
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