HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization

2026-07-08

AI Summary

This work addresses the limited out-of-distribution generalization and spurious floating-material artifacts in existing deep generative models for topology optimization, which stem from insufficient physical guidance. To overcome these issues, the authors propose a Hierarchical Physics-Guided Diffusion framework (HPG-Diff) that aligns precomputed physical features with the denoising process to optimize load-transfer paths. Additionally, a differentiable connectivity constraint based on virtual heat conduction is introduced to suppress disconnected structures. By innovatively integrating hierarchical physical guidance with a differentiable connectivity loss, the method simultaneously enhances both physical consistency and topological connectivity within the diffusion model. Experiments demonstrate that HPG-Diff achieves average compliance errors of only 0.87% and 5.29% on in-distribution and out-of-distribution tests, respectively, while reducing floating material ratios to 2.90% and 2.44%, and exhibits strong adaptability to non-rectangular design domains.

Abstract

Deep generative models offer a promising paradigm for topology optimization, enabling rapid design exploration. However, these approaches lack intrinsic physics guidance, often leading to poor generalizability across unseen boundary conditions and the formation of floating material artifacts. To address these limitations, we propose Hierarchical Physics-Guided Diffusion (HPG-Diff), a novel diffusion framework that enforces physics consistency through two synergistic mechanisms. First, we introduce a hierarchical physics-guided strategy that aligns different precomputed physics features with the denoising process, guiding material distribution toward optimal load paths to enhance generalizability. Second, we propose a floating material suppression loss as a differentiable connectivity constraint inspired by thermal conduction to improve topological connectivity. By simulating a virtual heat propagation process from load positions, this mechanism explicitly penalizes floating material during training. Quantitative evaluations demonstrate that HPG-Diff achieves average compliance errors of 0.87% (in-distribution) and 5.29% (out-of-distribution), while reducing floating material ratios to 2.90% and 2.44%, respectively. Furthermore, case studies on a 3:1 rectangular domain, including cantilever and bridge benchmarks, provide preliminary evidence that lightweight LoRA fine-tuning with a small dataset can support the adaptation of HPG-Diff to rectangular non-square domains.

Problem

• topology optimization
• physics guidance
• floating material
• generalizability
• deep generative models

Innovation

• physics-guided diffusion
• topology optimization
• differentiable connectivity constraint
• floating material suppression
• hierarchical denoising