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

arXiv: https://arxiv.org/abs/2502.01989 · HTML: https://mlsanity.com/paper/2502.01989/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)
- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [A Configurable Library for Generating and Manipulating Maze Datasets](https://mlsanity.com/paper/2309.10498/) (2023)

## Built on by (most cited first, 6 of 6)

- [Test-time scaling of diffusions with flow maps](https://mlsanity.com/paper/2511.22688/) (2025)
- [Training-Free Adaptation of Diffusion Models via Doob's h-Transform](https://mlsanity.com/paper/2602.16198/) (2026)
- [Adaptive Inference-Time Scaling via Cyclic Diffusion Search](https://mlsanity.com/paper/2505.14036/) (2025)
- [Probing Visual Planning in Image Editing Models](https://mlsanity.com/paper/2604.22868/) (2026)
- [Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement](https://mlsanity.com/paper/2605.19317/) (2026)
- [Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories](https://mlsanity.com/paper/2609.22867/) (2026)

## Abstract (arXiv)

Inspired by human SYSTEM 2 thinking, LLMs excel at complex reasoning tasks via extended Chain-of-Thought. However, similar test-time scaling for diffusion models to tackle complex reasoning remains largely unexplored. From existing work, two primary challenges emerge in this setting: (i) the dependence on an external verifier indicating a notable gap from intrinsic reasoning of human intelligence without any external feedback, and (ii) the lack of an efficient search algorithm. In this paper, 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. Concretely, VFScale comprises two key innovations to address the aforementioned challenges. On the training side, VFScale consists of a novel MRNCL loss and a KL regularization to improve the energy landscape, ensuring that the learned energy function itself serves as a reliable verifier. On the inference side, VFScale integrates the denoising process with a novel hybrid Monte Carlo Tree Search (hMCTS) to improve search efficiency. On challenging reasoning tasks of Maze and Sudoku, we demonstrate the effectiveness of VFScale's training objective and scalable inference method. In particular, trained with Maze sizes of up to 6×6, our VFScale solves 88% of Maze problems with much larger sizes of 15×15, while standard diffusion models completely fail. The code can be found at https://github.com/AI4Science-WestlakeU/VFScale.