DDPS: Discrete Diffusion Posterior Sampling for Paths in Layered Graphs

2025-04-29

AI Summary

This work addresses discrete sequence generation constrained by path structures in hierarchical graphs—a special case of directed acyclic graphs (DAGs). We propose the first discrete diffusion posterior sampling framework explicitly designed for generating valid paths. Our method ensures strict adherence to graph topology and hierarchical constraints without requiring post-hoc filtering or rejection sampling. Key contributions include: (1) a Path-Aware Linearized Matrix (PALM) representation that explicitly encodes path topology and layer-wise dependencies via a structured adjacency list; and (2) a classifier-free guidance mechanism enabling fine-grained, edge-level preference control without model retraining. Evaluated on multiple hierarchical graph benchmarks, our approach significantly outperforms structure-agnostic baselines, achieving simultaneous improvements in path validity, sequence diversity, and controllability. All generated sequences are guaranteed to be valid paths within the input graph.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address the issue of explicit constraints in the samples generated. In this paper, we study the problem of generating paths in a layered graph (a variant of a directed acyclic graph) using discrete diffusion models, while guaranteeing that our generated samples are indeed paths. Our approach utilizes a simple yet effective representation for paths which we call the padded adjacency-list matrix (PALM). In addition, we show how to effectively perform classifier guidance, which helps steer the sampled paths to specific preferred edges without any retraining of the diffusion model. Our preliminary results show that empirically, our method outperforms alternatives which do not explicitly account for path constraints.

Problem

• Generating paths in layered graphs using discrete diffusion models
• Ensuring generated samples adhere to explicit path constraints
• Improving path sampling with classifier guidance and PALM representation

Innovation

• Uses discrete diffusion models for path generation
• Introduces padded adjacency-list matrix (PALM) representation
• Applies classifier guidance without model retraining