VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model (ICLR 2026)

Here is the official implementation for VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model.

[paper][arXiv]

We introduce we introduce the Verifier-free Test-time Scalable Diffusion Model (VFScale) to achieve scalable intrinsic reasoning, which equips number-of-sample test-time scaling with the intrinsic energy function of diffusion models as the verifier. Trained with Maze tasks of up to 6x6, VFScale can generalize to solve much harder 15x15 Maze tasks, with larger test-time compute resulting in higher accuracy:

Framework of VFScale:

1. Environment Setup

conda env create -f environment.yml
conda activate VFScaleEnv
pip install -e .

2. Dataset and checkpoints

The datasets and checkpoints can be downloaded from this link.

3. Training

To train the model, run the following command

sh scripts/Maze_train.sh

sh scripts/Sudoku_train.sh

4. Inference

sh scripts/Maze_inference.sh

sh scripts/Sudoku_inference.sh

Citation

If you find our work and/or our code useful, please cite us via:

@inproceedings{
  zhang2026vfscale,
  title={{VFS}cale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model},
  author={Tao Zhang and Jia-Shu Pan and Ruiqi Feng and Tailin Wu},
  booktitle={The Fourteenth International Conference on Learning Representations},
  year={2026},
  url={https://openreview.net/forum?id=8ta0xgtsJK}
}