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

2026-03-15

AI Summary

This work proposes Chain-of-Trajectories (CoTj), a training-free framework that introduces System 2–style deliberative planning into diffusion sampling to overcome the inefficiency of fixed, content-agnostic scheduling in navigating high-dimensional noise manifolds. CoTj extracts low-dimensional semantic features via Diffusion DNA and reformulates the sampling process as a path-planning problem on a directed acyclic graph. By adopting a predict–plan–execute paradigm, it enables context-aware dynamic allocation of computational resources. Experiments demonstrate that CoTj consistently enhances generation quality and stability across diverse diffusion models while reducing redundant computations, thereby achieving efficient, resource-aware sampling.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• diffusion models
• trajectory planning
• state dimensionality
• computational misallocation
• sampling schedule

Innovation

• Chain-of-Trajectories
• Diffusion DNA
• graph-theoretic planning
• adaptive sampling
• System 2 reasoning