Contrastive Diffusion Guidance for Spatial Inverse Problems

2025-09-30

AI Summary

This work addresses the ill-posed inverse problem of reconstructing indoor spatial layouts (e.g., floorplans) from mobile trajectories. Due to the non-differentiable and non-invertible nature of forward path planning, conventional diffusion models struggle to stably guide generation. To overcome this, we propose CoGuide: a framework that reconstructs likelihood scores in a smooth embedding space learned via contrastive learning, enabling proxy estimation of intractable likelihood gradients; it jointly integrates contrastive learning, diffusion modeling, and non-differentiable simulation to effectively steer the denoising process. Experiments demonstrate that CoGuide generates floorplans significantly more faithful to real trajectory distributions, achieving superior robustness and geometric consistency compared to differentiable-planning baselines and standard guided diffusion approaches.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Diffusion Models for Vision
• Intelligent Robots: Localization, Mapping, and Navigation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Problem

• Reconstructing spatial layouts from movement trajectories
• Solving ill-posed inverse problems with diffusion models
• Handling non-differentiable forward operators via contrastive embeddings

Innovation

• Uses diffusion-based posterior sampler for layouts
• Trains contrastive embedding space for compatibility
• Approximates likelihood score to steer denoising process