---
title: 'DALI-PD: Diffusion-Based PD Heatmap Generation'
url: https://www.emergentmind.com/topics/dali-pd
type: topic
---

# DALI-PD: Diffusion-Based PD Heatmap Generation

Searching arXiv for the primary DALI-PD paper and closely related work on PD datasets and diffusion pretraining.
DALI-PD is a framework for generating synthetic layout heatmaps for machine learning in physical design. It was introduced to address a central bottleneck in PD-oriented ML: the scarcity of high-quality, large-scale training data, especially for tasks such as IR drop prediction and congestion estimation. The framework uses a diffusion model to generate diverse heatmaps in seconds, rather than requiring hours of placement-and-routing and signoff analysis per sample, and was reported to produce heatmaps that closely resemble real layouts while improving downstream ML accuracy on tasks such as IR drop or congestion prediction [2507.10606].

## 1. Definition, scope, and problem setting

In the PD context, DALI-PD denotes “Diffusion-based Synthetic Layout Heatmap Generation for ML in Physical Design” [2507.10606]. Its stated goal is fast, scalable generation of synthetic layout heatmaps that are statistically similar to real layouts and useful for downstream ML. The motivating constraints are threefold. First, realistic heatmaps such as IR drop and congestion require full P\&R and signoff flows, and per-sample runtimes are hours on commercial tools. Second, industrial datasets are usually proprietary, and released datasets are often obfuscated to protect IP, which distorts distributions. Third, public datasets are typically static and slow to refresh as tools, nodes, and design styles evolve [2507.10606].

The framework is positioned as an alternative to direct expansion of datasets such as CircuitNet. Rather than generating new layouts by rerunning expensive EDA flows, DALI-PD synthesizes the heatmap modality directly. This suggests a shift from “design-flow-driven dataset construction” to “generative-model-driven dataset construction,” with the intended benefit of broader design-space coverage under substantially lower marginal generation cost.

The system targets variation in area, aspect ratio, utilization, macro count and placement, and clock period. The paper reports a generated dataset of 23,070 synthetic layout configurations spanning area \(500~\mu\mathrm{m} \times 500~\mu\mathrm{m}\) to \(1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}\), aspect ratio \(1\)–\(2\), utilization \(60\%\)–\(90\%\), macro count \(1\)–\(50\), and user-specified clock periods [2507.10606].

## 2. Generated modalities and conditioning interface

DALI-PD generates six co-registered channels per layout, aligned with the modalities used in CircuitNet [2507.10606].

| Channel | Semantics | Normalization / analysis note |
|---|---|---|
| Cell density | Number of placed standard cells per grid bin | Normalized to \([0,1]\); “low-density” defined as \(< 0.1\) |
| Macro region | Binary mask indicating macro bounding boxes | \(\{0,1\}\); evaluated via pixelwise L1 and SSIM |
| RUDY | Placement-stage proxy for routing demand | Normalized to \([0,1]\); “hotspots” defined as \(> 0.9\) |
| IR drop | Voltage drop on the power grid | Normalized to \([0,1]\); can be rescaled post hoc |
| Power | Total power density | Normalized to \([0,1]\); “hotspots” defined as \(> 0.9\) |
| Toggle rate–scaled power | Dynamic power scaled by toggle activity | Normalized to \([0,1]\); “hotspots” defined as \(> 0.9\) |

All channels are generated on the same spatial grid. CircuitNet heatmaps have width and height in \([222,314]\) pixels with \(2.25~\mu\mathrm{m}\) per pixel, and DALI-PD maintains this granularity while allowing arbitrary user-specified \(H \times W\) at inference [2507.10606].

The conditioning interface is circuit- and floorplan-aware. At inference, the specified inputs are layout height \(H\), width \(W\), utilization \(u\), clock period \(c\), macro count \(M\), and macro bounding boxes \(B\), where bounding boxes are normalized by \(H\) and \(W\). A circuit encoding module creates a token sequence \(L\) of length \(k \ge M\) with learnable projections for \((c,u)\) and for each macro’s \((x_l,y_l,x_u,y_u)\). If \(M < k\), the remaining tokens are padded with zeros, while \((c,u)\) are repeated to fill \(k\) [2507.10606].

This conditioning design places DALI-PD closer to structured conditional generation than to unconditional image synthesis. A plausible implication is that the framework is intended not merely to reproduce empirical heatmap statistics, but to preserve control over floorplan-level determinants of those statistics.

## 3. Generative architecture and mathematical formulation

DALI-PD uses a two-stage latent diffusion pipeline: a variational autoencoder followed by a latent diffusion U-Net [2507.10606].

The VAE is trained from scratch for six-channel, non-RGB PD images. Its encoder maps six input channels to a latent representation with \(d_{\mathrm{latent}} = 4\) using ResNet downsampling blocks, and its decoder reconstructs six-channel heatmaps through ResNet upsampling blocks. The objective is an ELBO with KL regularization to a Gaussian latent prior [2507.10606].

The diffusion stage operates in VAE latent space. The paper gives the standard DDPM forward process:
$$
q(x_t \mid x_{t-1}) = \mathcal{N}(x_t; \sqrt{1-\beta_t}\,x_{t-1}, \beta_t I),
$$
with
$$
x_t = \sqrt{\bar{\alpha}_t}\,x_0 + \sqrt{1-\bar{\alpha}_t}\,\epsilon,
$$
where \(\alpha_t = 1-\beta_t\), \(\bar{\alpha}_t = \prod_{s=1}^{t}\alpha_s\), and \(\epsilon \sim \mathcal{N}(0,I)\) [2507.10606].

The reverse process is parameterized as
$$
p_\theta(x_{t-1} \mid x_t, c) = \mathcal{N}(x_{t-1}; \mu_\theta(x_t,t,c), \sigma_t^2 I),
$$
with an \(\epsilon\)-predictor \(\epsilon_\theta(x_t,t,c)\) and DDPM mean
$$
\mu_\theta(x_t,t,c) = \frac{1}{\sqrt{\alpha_t}}\left(x_t - \frac{\beta_t}{\sqrt{1-\bar{\alpha}_t}}\,\epsilon_\theta(x_t,t,c)\right).
$$
The inference step is reported as
$$
x_{t-1} = \frac{1}{\sqrt{\alpha_t}}\left(x_t - \frac{1-\alpha_t}{\sqrt{1-\bar{\alpha}_t}}\,\epsilon_\theta(x_t,t,c)\right) + \sigma_t z,
$$
with \(z \sim \mathcal{N}(0,I)\) for \(t>1\) [2507.10606].

The simplified training objective is
$$
L_{\mathrm{simple}} = \mathbb{E}_{x_0,t,\epsilon}\left[\left\| \epsilon - \epsilon_\theta\!\left(\sqrt{\bar{\alpha}_t}x_0 + \sqrt{1-\bar{\alpha}_t}\epsilon, t, c\right)\right\|_2^2\right].
$$
Conditioning is injected via cross-attention, replacing CLIP text tokens in DiffusionSat with circuit embedding tokens \(L \in \mathbb{R}^{k \times d_L}\). The paper describes the attention as
$$
\mathrm{Attn}(Q,K,V) = \mathrm{softmax}\left(\frac{QK^T}{\sqrt{d_{\mathrm{attn}}}}\right)V,
$$
with latent features forming the queries and the circuit tokens providing keys and values [2507.10606].

Inference uses a DDPM sampler with 100 steps and guidance scale \(1.0\), producing accepted samples in \(1\)–\(2\) seconds [2507.10606]. Post-processing heuristics sharpen macro edges and align cells and power distributions to reduce image-like artifacts, and a checker enforces user constraints such as utilization; invalid samples, including overlapping macros, are discarded and re-sampled [2507.10606].

## 4. Training data, transfer initialization, and dataset construction

The real-data source is CircuitNet at \(28\,\mathrm{nm}\), comprising six RTL designs with layouts generated under varying P\&R options, utilizations, and clocks [2507.10606]. The reported train/test protocol is deliberately extrapolative. Training designs are RISCY-a, RISCY-FPU-a, RISCY-b, and RISCY-FPU-b, with macro counts \(4\), \(5\), \(13\), and \(14\). Training utilizations are \(\{70,75,80,85\}\%\), and training clocks are \(\{2,5\}\,\mathrm{ns}\). Test designs are zero-riscy-a and zero-riscy-b, with macro counts \(3\) and \(15\), test-only utilization \(90\%\), and test-only clock \(20\,\mathrm{ns}\) [2507.10606].

The training set contains 2,861 unique datapoints, expanded by flip/rotation augmentations by \(11\times\) to 34,332. The test set contains 67 samples [2507.10606]. The VAE is trained from scratch for 550K steps, while the latent diffusion U-Net and circuit encoder are trained for 140K steps. Optimization uses AdamW and an EMA of weights, with one NVIDIA A6000 GPU per training run [2507.10606].

A notable design choice is transfer initialization from DiffusionSat rather than from a generic Stable Diffusion model. The paper reports that this satellite-image initialization improves both fidelity and sampling efficiency relative to the Stable Diffusion–initialized baseline. Specifically, DALI-PD with DiffusionSat initialization achieves average FID \(41.86\) versus \(70.29\) for the Stable Diffusion baseline, and requires \(2.68\) iterations on average to pass the checker versus \(24\) for the baseline [2507.10606]. This suggests that the model benefits from pretraining on imagery with large-scale spatial structure and multi-channel geospatial texture, which is closer to PD heatmaps than natural-image priors are.

At dataset scale, DALI-PD generated 23,070 samples in 4 hours on \(8\times\) NVIDIA L40S plus \(4\times\) NVIDIA A6000 GPUs [2507.10606]. Relative to hours-per-sample EDA generation, this throughput is one of the framework’s principal practical claims.

## 5. Evaluation, diversity, and downstream ML utility

The paper evaluates DALI-PD along three axes: statistical similarity to real layouts, intra-dataset diversity, and utility for downstream prediction tasks [2507.10606].

On similarity metrics, DALI-PD is reported to match test-set distributions closely for IR drop and power, including toggle-scaled power, while RUDY shows mild skew because it is sensitive to geometry. Pixelwise L1 on 67 matched-condition test pairs yields average errors of \(0.09\) for cell density, \(0.26\) for macro region, \(0.17\) for RUDY, \(0.17\) for IR drop, \(0.04\) for power, and \(0.02\) for scaled power [2507.10606]. The hotspot and low-density statistics are likewise close to the real set: low cell density \((<0.1)\) is \(58.83\%\) in test data versus \(62.78\%\) in DALI-PD; RUDY hotspots \((>0.9)\) are \(1.2\%\) versus \(0.68\%\); IR-drop hotspots are \(0.03\%\) versus \(0.01\%\) [2507.10606].

Diversity is assessed by pairwise SSIM over 1,000 generated samples per channel, totaling 499,500 pairs. Reported average pairwise SSIMs are \(0.233\) for cell density, \(0.246\) for macro, \(0.233\) for RUDY, \(0.250\) for IR drop, \(0.288\) for power, and \(0.318\) for scaled power, with all pairs below \(0.45\) [2507.10606]. CircuitNet has higher pairwise SSIM in several channels, including \(0.423\) for macro region, indicating less variation than the synthetic dataset [2507.10606]. The t-SNE analysis further shows DALI-PD covering regions absent from training and test data, which the paper interprets as increased design-space coverage.

For downstream ML, the paper studies two U-Net predictors. IR-drop prediction uses cell density, power, and toggle-scaled power as inputs with IR drop as target; RUDY prediction uses cell density and macro region as inputs with RUDY as target. The predictor architecture uses kernel size \(5\), channels \([16,64,128,512]\), learning rate \(5\times 10^{-5}\), batch size \(64\), and 125 training steps [2507.10606].

Training solely on DALI-PD is competitive with, but generally weaker than, training on real CircuitNet data: for IR drop, real-data training yields L1 / hotspot L1 of \(0.036 / 0.085\), while DALI-PD training yields \(0.062 / 0.14\); for RUDY, real-data training yields \(0.067 / 0.202\), while DALI-PD yields \(0.092 / 0.168\) [2507.10606]. The notable result is data efficiency: pretraining on DALI-PD and then fine-tuning with fewer than 500 real heatmaps outperforms training on the limited real data alone [2507.10606]. This is the core empirical argument for the framework: synthetic data are not presented as a signoff substitute, but as a mechanism for improving representation learning when real PD data are scarce.

## 6. Limitations, usage profile, and research significance

The paper identifies several limitations. Macro mask fidelity is weaker than that of other channels, reflected in macro-region average L1 \(=0.26\), and generated masks can exhibit overly sharp or slightly overlapping edges. RUDY also shows a modest distributional skew because of its sensitivity to geometry. Moreover, all generation occurs in normalized \([0,1]\) space, so mapping outputs back to physical units requires domain-specific calibration. The framework is explicitly not positioned as a replacement for signoff analysis [2507.10606].

Generalization across technology nodes is not claimed. Training is performed on \(28\,\mathrm{nm}\) CircuitNet, and cross-node deployment would require adaptation or fine-tuning [2507.10606]. Unusual macro placements, especially extreme clustering, may trigger rejection and re-sampling. These points limit any interpretation of DALI-PD as a universal PD simulator; it is more precisely a conditional generative prior over a particular family of heatmap distributions.

In practical use, the recommended workflow is to specify \(H\), \(W\), \(u\), \(c\), \(M\), and macro boxes \(B\), run the DDPM reverse process for \(T=100\) steps with cross-attention on the circuit token sequence, decode through the VAE, and then apply post-processing plus checker-based rejection if utilization or non-overlap constraints are violated [2507.10606]. The generated outputs are six normalized channels, which can be fed directly into downstream ML pipelines or selectively rescaled.

The broader significance of DALI-PD lies in its redefinition of dataset generation for PD ML. Earlier synthetic-generation approaches cited in the paper were narrower: BeGAN generated only power maps at fixed sizes, while tools such as ANG still require P\&R to derive heatmaps [2507.10606]. DALI-PD instead synthesizes six channels jointly, supports variable sizes and structured conditioning, and uses diffusion rather than GAN-based generation. This suggests an emerging research direction in which PD ML datasets are produced through controllable, multimodal generative models rather than by repeated execution of expensive backend flows.

The open-sourced code and 23,070-sample synthetic dataset extend that direction beyond a proof of concept [2507.10606]. Within the literature represented by the paper, DALI-PD is best understood as a synthetic-data infrastructure layer for physical-design ML: not a replacement for real layouts, but a scalable conditional generator intended to enlarge training support, improve generalization, and reduce dependence on scarce, IP-constrained, and computationally expensive real-world PD corpora.

Source: https://www.emergentmind.com/topics/dali-pd