Chain-of-Trajectories: Unlocking the Intrinsic Generative Optimality of Diffusion Models via Graph-Theoretic Planning

TL;DR

This paper introduces Chain-of-Trajectories (CoTj), a planning framework for diffusion models that improves output quality and efficiency by dynamically allocating computational effort based on a low-dimensional difficulty signature.

Contribution

We propose CoTj, a novel graph-based planning approach that enables deliberative, resource-aware sampling in diffusion models, addressing the rigidity of traditional fixed schedules.

Findings

CoTj improves image quality and stability in diffusion models.

It reduces redundant computation during sampling.

CoTj demonstrates effective trajectory planning in high-dimensional spaces.

Abstract

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.