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This paper introduces HPG-Diff, a novel diffusion framework for topology optimization that integrates hierarchical physics guidance and a floating material suppression loss to enhance design generalizability and connectivity. By aligning precomputed physics features with the denoising process, HPG-Diff effectively directs material distribution towards optimal load paths, while the connectivity constraint mitigates the formation of floating material artifacts. Quantitative results show that HPG-Diff significantly reduces compliance errors and floating material ratios, demonstrating its effectiveness in both in-distribution and out-of-distribution scenarios.
HPG-Diff achieves remarkable compliance errors of just 0.87% in-distribution while drastically reducing floating material ratios, transforming topology optimization practices.
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.
