# CLDRoute: Conditional Latent Diffusion for Routability Map Generation in Physical Design

arXiv: https://arxiv.org/abs/2607.16674 · HTML: https://mlsanity.com/paper/2607.16674/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Generalizable Cross-Graph Embedding for GNN-based Congestion Prediction](https://mlsanity.com/paper/2111.05941/) (2021)
- [Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealing](https://mlsanity.com/paper/2310.15440/) (2023)

## Abstract (arXiv)

Accurate routability estimation during physical design is important for reducing costly post-routing iterations. Prior learning-based methods treat this task as deterministic prediction, mapping placement-stage features to a single congestion or DRC outcome. We instead formulate routability estimation as a conditional generation problem, where both routing congestion and DRC violations are modeled as spatially structured routability fields. Our framework, Conditional Latent Diffusion for Routeability estimation (CLDRoute), uses physics-aware conditioning and task-specific latent modeling to handle the different characteristics of congestion and DRC maps. This allows our method to supports sample-based inference, producing both a mean prediction and a spatial uncertainty estimate for the same input design. On CircuitNet 2.0 (N28), our method achieves, for DRC violation generation, an SSIM of 0.9678, an MAE of 0.0028, and a TopK@1% of 0.3494; for congestion generation, it achieves an SSIM of 0.9031, an MAE of 0.0286, and an NZ-Pearson of 0.3692. Overall, our framework provides a more practical view of routability at placement by generating both the expected outcome and its uncertainty.