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VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 1 citations (OpenAlex)

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Proposes VFScale, a verifier-free test-time scaling framework for energy-based diffusion models that uses the learned energy as a verifier, trained with MRNCL and KL losses and searched with a hybrid BoN/MCTS denoising procedure, evaluated on Maze and Sudoku reasoning.

Problem

Diffusion models for complex reasoning do not scale well at test time: performance plateaus with more sampling steps, and existing number-of-sample scaling relies on external verifiers, while learned energy functions are poorly aligned with solution quality.

Approach

Uses the diffusion model's intrinsic energy as a verifier, trains it with a Monotonic-Regression Negative Contrastive Learning loss (energy linear in L2 distance of corrupted negatives) plus a per-step KL regularizer, and searches with hybrid BoN-then-MCTS denoising.

Key results

• On 15x15 Maze, VFScale with hMCTS denoising reaches 88.28% success at N=161 versus 10.9% for original energy-based diffusion with BoN.
• On Sudoku with 33 givens, the full VFScale training yields 19.5% at N=1 versus 32.0% for original training, but with hMCTS and larger N it reaches 42.97% at N=321 on the harder set.
• Performance-energy consistency rises from about 73% (original) to about 84% when MRNCL is added (w/o KL variant).

Surprising findings

• The full VFScale model underperforms its ablated variants at N=1 on Maze and Sudoku, which the authors frame as a deliberate trade-off for better scalability.
• A trained external classifier verifier performs substantially worse than the intrinsic energy verifier under BoN (about 35% vs 59-69% at N=11-81 on 15x15 Maze).

Limitations

• Evaluated only on Maze and Sudoku, synthetic reasoning tasks.
• Full model underperforms ablations at N=1 on the naive setting.
• Success rates on the hardest Sudoku remain under 45% even with large budgets.

Experimental setup

Datasets: Maze DFS-generated mazes (sizes 4-6 for training; 6-30 for testing) SAT-Net Sudoku RRN Sudoku (harder test set)

Benchmarks: Maze (grid sizes 6-15, out-of-distribution) Sudoku harder RRN dataset (17-33 givens)

Metrics: solving success rate performance-energy consistency

Baselines: Original energy-based diffusion Original BoN BoN with ground-truth guidance external learned verifier sparse GT 0/1 verifier

Builds on: energy-based diffusion for reasoning contrastive energy learning AlphaGo MCTS DDIM

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