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

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 $6\times6$, our VFScale solves 88% of Maze problems with much larger sizes of $15\times15$, while standard diffusion models completely fail. The code can be found at https://github.com/AI4Science-WestlakeU/VFScale.