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DSBRouter: End-to-end Global Routing via Diffusion Schr\"{o}dinger Bridge
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Proposes DSBRouter, an end-to-end neural global router that learns forward and backward bridges between initial pins and routes via a Diffusion Schrödinger Bridge, with evaluation-based guidance at inference to reduce overflow without post-processing.
Problem
Global routing in VLSI chip design needs connected routes, but learned generative routers lack a mechanism guaranteeing connectivity, so they rely on post-processing search or RL.
Approach
Models the pin-to-route transition as a Diffusion Schrödinger Bridge learning both directions between pins and routes, and steers backward sampling with gradients from an overflow-based objective score (evaluation-based guidance), yielding connected routes end-to-end.
Key results
- On ISPD98 ibm01-05, DSBRouter reduces total overflow sharply versus NeuralSteiner, averaging a 90.4% reduction and reaching 100% on ibm02, ibm05, ada03, ada04.
- On the ISPD07 small-4/small/large-4/large cases, DSBRouter achieves 1.000 correctness rate while all HubRouter variants without RL post-processing reach at most 0.44.
- DSBRouter is much slower, taking roughly 4491 to 125589 seconds per benchmark, versus seconds to minutes for classical and HubRouter baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DSBRouter rather than NeuralSteiner | Global routing · IBM01 | overflow: 2200 -> 1430 | Helped |
| use DSBRouter rather than NeuralSteiner | Global routing · IBM02, IBM03, IBM04, IBM05, ADA03, ADA04 | overflow: 3800 -> 0; 2100 -> 4; 2700 -> 10; 18 -> 0; 728 -> 0; 97 -> 0 | Helped |
| use DSBRouter rather than Geosteiner | Global routing · IBM01, IBM02, IBM03, IBM04, IBM05, ADA03, ADA04 | wirelength: 60142 -> 61435; 165863 -> 174016; 145678 -> 152862; 162734 -> 163942; 409709 -> 420464; 9330748 -> 29478326; 8865643 -> | Mixed |
| add gradient guidance (ablation) | DSBRouter · IBM01 | overflow: 3561 -> 1430 | Helped |
| add gradient guidance (ablation) | DSBRouter · IBM01 | wirelength: 61003 -> 61435 | Mixed |
| add neural network (ablation) | DSBRouter · IBM01 | overflow: 5971 -> 1430 | Helped |
| add neural network (ablation) | DSBRouter · IBM01 | wirelength: 75975 -> 61435 | Helped |
| increase inference steps from 10 to 50 (ablation) | DSBRouter · IBM01 | overflow: 924 -> 421 | Helped |
| increase inference steps from 10 to 50 (ablation) | DSBRouter · IBM01 | wirelength: 64237 -> 70172 | Hurt |
| increase inference steps from 10 to 50 (ablation) | DSBRouter · IBM01 | inference time: 2774 -> 10881 | Hurt |
| increase training depth from 64 to 192 with 24 inference steps (ablation) | DSBRouter · IBM01 | wirelength: 68982 -> 61433 | Helped |
| increase training depth from 64 to 192 with 24 inference steps (ablation) | DSBRouter · IBM01 | overflow: 784 -> 1428 | Hurt |
Surprising findings
- On ada03 and ada04 DSBRouter produces substantially longer wirelength than NeuralSteiner (about 29.5M vs 9.5M and 24.3M vs 9.0M) in exchange for lower overflow.
- Without the guidance module, the model cannot guarantee connectivity and needs Geosteiner post-processing.
Limitations
- Inference is very slow due to many sampling steps and gradient computation; accelerated samplers like DDIM cannot be applied.
- Wirelength is longer than some baselines on ISPD07 large benchmarks.
- Training uses a fixed 64x64 figure size.
Experimental setup
Datasets: ISPD07 NTHURouter-generated routes ISPD98
Benchmarks: ISPD98 (ibm01-05) ISPD07 (adaptec3, adaptec4)
Metrics: overflow wirelength correctness rate wirelength ratio generation time
Baselines: GeoSteiner Labyrinth FLUTE+ES HubRouter (VAE) HubRouter (GAN) HubRouter (DPM) NeuralSteiner DRL
Builds on: Diffusion Schrödinger Bridge Tang et al. 2024 terminal reparameterized DSB HubRouter classifier guidance
Closest papers by meaning
- NeuralSteiner: Learning Steiner Tree for Overflow-avoiding Global Routing in Chip Design (NeurIPS 2024 · similarity 0.90)
- GLOP: Learning Global Partition and Local Construction for Solving Large-Scale Routing Problems in Real-Time (AAAI 2024 · similarity 0.83)
- PreRoutGNN for Timing Prediction with Order Preserving Partition: Global Circuit Pre-training, Local Delay Learning and Attentional Cell Modeling (AAAI 2024 · similarity 0.83)
- Chip Placement with Diffusion Models (ICML 2025 · similarity 0.82)
- Learning to Solve Compositional Geometry Routing Problems (NeurIPS 2026 · similarity 0.82)
- SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver (NeurIPS 2026 · similarity 0.82)
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