DALI-PD: Diffusion-Based PD Heatmap Generation

• DALI-PD is a conditional generative framework that synthesizes layout heatmaps using a two-stage latent diffusion process mimicking full placement-and-routing flows.
• It generates six co-registered channels with structured conditioning to accurately simulate IR drop, power, and congestion characteristics.
• The framework dramatically speeds up data generation, producing large-scale datasets that improve downstream ML accuracy with validated statistical similarity to real layouts.

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 (Wu et al., 13 Jul 2025).

1. Definition, scope, and problem setting

In the PD context, DALI-PD denotes “Diffusion-based Synthetic Layout Heatmap Generation for ML in Physical Design” (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025).

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 (Wu et al., 13 Jul 2025).

2. Generated modalities and conditioning interface

DALI-PD generates six co-registered channels per layout, aligned with the modalities used in CircuitNet (Wu et al., 13 Jul 2025).

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	$1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$0; evaluated via pixelwise L1 and SSIM
RUDY	Placement-stage proxy for routing demand	Normalized to $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$1; “hotspots” defined as $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$2
IR drop	Voltage drop on the power grid	Normalized to $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$3; can be rescaled post hoc
Power	Total power density	Normalized to $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$4; “hotspots” defined as $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$5
Toggle rate–scaled power	Dynamic power scaled by toggle activity	Normalized to $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$6; “hotspots” defined as $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$7

All channels are generated on the same spatial grid. CircuitNet heatmaps have width and height in $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$8 pixels with $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$9 per pixel, and DALI-PD maintains this granularity while allowing arbitrary user-specified $1$0 at inference (Wu et al., 13 Jul 2025).

The conditioning interface is circuit- and floorplan-aware. At inference, the specified inputs are layout height $1$1, width $1$2, utilization $1$3, clock period $1$4, macro count $1$5, and macro bounding boxes $1$6, where bounding boxes are normalized by $1$7 and $1$8. A circuit encoding module creates a token sequence $1$9 of length $2$0 with learnable projections for $2$1 and for each macro’s $2$2. If $2$3, the remaining tokens are padded with zeros, while $2$4 are repeated to fill $2$5 (Wu et al., 13 Jul 2025).

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 (Wu et al., 13 Jul 2025).

The VAE is trained from scratch for six-channel, non-RGB PD images. Its encoder maps six input channels to a latent representation with $2$6 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 (Wu et al., 13 Jul 2025).

The diffusion stage operates in VAE latent space. The paper gives the standard DDPM forward process:

$2$7

with

$2$8

where $2$9, $60\%$0, and $60\%$1 (Wu et al., 13 Jul 2025).

The reverse process is parameterized as

$60\%$2

with an $60\%$3-predictor $60\%$4 and DDPM mean

$60\%$5

The inference step is reported as

$60\%$6

with $60\%$7 for $60\%$8 (Wu et al., 13 Jul 2025).

The simplified training objective is

$60\%$9

Conditioning is injected via cross-attention, replacing CLIP text tokens in DiffusionSat with circuit embedding tokens $90\%$0. The paper describes the attention as

$90\%$1

with latent features forming the queries and the circuit tokens providing keys and values (Wu et al., 13 Jul 2025).

Inference uses a DDPM sampler with 100 steps and guidance scale $90\%$2, producing accepted samples in $90\%$3–$90\%$4 seconds (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025).

4. Training data, transfer initialization, and dataset construction

The real-data source is CircuitNet at $90\%$5, comprising six RTL designs with layouts generated under varying P&R options, utilizations, and clocks (Wu et al., 13 Jul 2025). 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 $90\%$6, $90\%$7, $90\%$8, and $90\%$9. Training utilizations are $1$0, and training clocks are $1$1. Test designs are zero-riscy-a and zero-riscy-b, with macro counts $1$2 and $1$3, test-only utilization $1$4, and test-only clock $1$5 (Wu et al., 13 Jul 2025).

The training set contains 2,861 unique datapoints, expanded by flip/rotation augmentations by $1$6 to 34,332. The test set contains 67 samples (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025).

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 $1$7 versus $1$8 for the Stable Diffusion baseline, and requires $1$9 iterations on average to pass the checker versus $50$0 for the baseline (Wu et al., 13 Jul 2025). 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 $50$1 NVIDIA L40S plus $50$2 NVIDIA A6000 GPUs (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025).

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 $50$3 for cell density, $50$4 for macro region, $50$5 for RUDY, $50$6 for IR drop, $50$7 for power, and $50$8 for scaled power (Wu et al., 13 Jul 2025). The hotspot and low-density statistics are likewise close to the real set: low cell density $50$9 is $[0,1]$0 in test data versus $[0,1]$1 in DALI-PD; RUDY hotspots $[0,1]$2 are $[0,1]$3 versus $[0,1]$4; IR-drop hotspots are $[0,1]$5 versus $[0,1]$6 (Wu et al., 13 Jul 2025).

Diversity is assessed by pairwise SSIM over 1,000 generated samples per channel, totaling 499,500 pairs. Reported average pairwise SSIMs are $[0,1]$7 for cell density, $[0,1]$8 for macro, $[0,1]$9 for RUDY, $< 0.1$0 for IR drop, $< 0.1$1 for power, and $< 0.1$2 for scaled power, with all pairs below $< 0.1$3 (Wu et al., 13 Jul 2025). CircuitNet has higher pairwise SSIM in several channels, including $< 0.1$4 for macro region, indicating less variation than the synthetic dataset (Wu et al., 13 Jul 2025). 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 $< 0.1$5, channels $< 0.1$6, learning rate $< 0.1$7, batch size $< 0.1$8, and 125 training steps (Wu et al., 13 Jul 2025).

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 $< 0.1$9, while DALI-PD training yields $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$00; for RUDY, real-data training yields $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$01, while DALI-PD yields $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$02 (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025). 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 $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$03, 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 $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$04 space, so mapping outputs back to physical units requires domain-specific calibration. The framework is explicitly not positioned as a replacement for signoff analysis (Wu et al., 13 Jul 2025).

Generalization across technology nodes is not claimed. Training is performed on $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$05 CircuitNet, and cross-node deployment would require adaptation or fine-tuning (Wu et al., 13 Jul 2025). 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 $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$06, $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$07, $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$08, $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$09, $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$10, and macro boxes $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$11, run the DDPM reverse process for $1200~\mu\mathrm{m} \times 1200~\mu\mathrm{m}$12 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 (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025). 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 (Wu et al., 13 Jul 2025). 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.