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From Generation to Discovery: Diffusion Mutation Kernels for Circuit and Physical Design
Dinithi Jayasuriya, Aravind Saravanan, Nilesh Ahuja, Amanda Rios, Amit Trivedi
TL;DR
Design discovery must produce novel, valid artifacts and improve established designs under external evaluation. The paper uses partial re-noising and denoising as diffusion mutation kernels, with conformal trajectory steering to discard unpromising candidates before expensive evaluation. Across three electronic design spaces, it discovers verified prefix adders, unseen amplifier topologies, and competitive macro placements.
Problem
Discovery requires novel artifacts that satisfy hard structural constraints and improve utility under evaluators the model cannot control.
Method
Diffusion mutation kernels transform existing artifacts through controlled re-noising and denoising, while external tools provide feasibility and performance judgments.
Results
Across three electronic design spaces, the framework discovers formally verified adders, seven unseen amplifier topologies, and macro placements reaching 0.68× an industrial placer’s wirelength.
Takeaways & Limitations
Diffusion models can serve as learned search operators while external evaluators remain the authority for feasibility and quality.
Takeaways & Limitations
The conformal guarantee is policy-specific, so changes to the generation, evaluation, checkpoint, or winner-definition protocol require recalibration.
Abstract
from arXiv · showhide
Generation and discovery are different problems. A generative model trained on valid artifacts reproduces a distribution, whereas discovery must produce artifacts that lie outside the observed corpus, satisfy hard structural constraints, and improve on established designs under evaluation that the model cannot influence. We introduce a diffusion-based discovery framework. Unlike conventional generative models that sample from learned distributions, it learns transition operators that transform existing artifacts into new candidates. Controlled partial re-noising followed by denoising defines a diffusion mutation kernel, a learned transition distribution that preserves the structural regularities of feasible designs while moving between regions of the design space. The learned model supplies feasibility structure only, and all correctness and performance judgments remain with external engineering tools. Intermediate diffusion trajectories are additionally monitored under a conformal risk budget so that unpromising candidates are discarded before expensive evaluation. We evaluate the framework on three electronic design spaces, an environment that supplies rigorous non-differentiable evaluators in the form of simulation, formal equivalence checking, and industrial physical implementation. The framework discovers 32-bit prefix adders that are formally verified equivalent to addition over all 2^64 input pairs and reduce delay by 17% and area by 18% relative to Kogge-Stone under a placed-and-timed flow; seven independently re-simulated amplifier topologies absent from the training corpus, spanning gains of 21.9-66.1 dB and bandwidths of 72.9 kHz-207 MHz; and macro placements on held-out netlists reaching 0.68x wirelength of an industrial placer.
1 Introduction
SteerGenSE reframes diffusion models as search operators for discovering novel, feasible designs rather than merely reproducing training distributions. It combines diffusion mutation, external engineering evaluation, and trajectory-aware steering across three electronic design spaces.
- Discovery must find novel artifacts that satisfy hard constraints and improve utility under evaluators the model does not control.
- Partial re-noising followed by denoising defines a diffusion mutation kernel that preserves parent structure while exploring learned design directions.The kernel converts a trained diffusion model into a search operator without additional training.
- 17% lower delay and 18% lower area than Kogge-Stone were achieved by 32-bit prefix adders under a placed-and-timed flow.The adders were formally verified before and after technology mapping.
- Seven amplifier topologies absent from training were independently re-simulated, and macro placements on held-out netlists reached 0.68× an industrial placer’s wirelength.
- External engineering tools judge feasibility, performance, and novelty, while trajectory-aware steering prunes unpromising paths and reallocates computation.Pareto selection carries the selected population into the next generation.
2 Relation to Prior Work
Prior work separates distribution learning from iterative search. SteerGenSE instead uses diffusion transitions between valid artifacts while retaining external evaluation for objective judgments.
- Generative design models learn p(x) and draw artifacts, whereas SteerGenSE uses the same network to realize p(x′|x) transitions between valid artifacts.
- The framework combines diffusion mechanisms such as partial denoising with simulation, implementation, and verification flows in an iterative discovery process.
3 Diffusion as a Learned Search Operator
The framework turns diffusion models into learned transition operators for constrained design discovery, while external engineering tools retain authority over feasibility and performance. Controlled steering and conformal pruning support search across heterogeneous design spaces while reducing costly evaluations.
- Discovery formulation: Discovery optimizes external performance and novelty subject to a hard validity predicate, producing a Pareto set rather than a single optimum.The formulation separates utility, novelty, and correctness constraints.
- Diffusion as a Learned Search Operator: Diffusion mutation kernels transform existing valid artifacts into candidates by partial re-noising and reverse denoising, without additional training.The kernel preserves parent structure while exploring learned directions within the model’s support.
- External evaluation: The model learns feasible transitions only; simulation, synthesis, implementation, and verification flows establish feasibility, correctness, and performance.This separation avoids replacing the evaluator with a learned objective surrogate.
- Mutation control: Small γ favors local refinement, whereas large γ enables broader exploration; the reported settings use γ = 0.3 for placement and prefix adders and γ = 0.5 for analog circuits.The re-noising depth controls the breadth of mutation.
- Trajectory-aware steering: Conformal steering prunes predicted-unpromising trajectories while reallocating released computation among survivors, but its payoff depends on evaluator cost and reliability of intermediate failure signals.The guarantee is policy-specific and requires recalibration when the generation, evaluation, checkpoint, or winner protocol changes.
- Cross-domain framework: The same discovery formulation and search process operate across discrete topology, symbolic architecture, and continuous spatial design spaces despite domain-specific representations and evaluators.The three settings vary in artifact representation, validity mechanism, and engineering evaluator.
4 Discovery Across Three Design Spaces
SteerGenSE applies one diffusion-based discovery formulation across prefix architectures, analog topologies, and macro placement, while external engineering flows determine validity and performance. Across these spaces, it produces novel verified, simulated, or placed designs under domain-specific evaluators.
- Cross-space framework: The unchanged discovery formulation spans symbolic topology, functional architecture, and continuous spatial design, despite different representations, validity predicates, and evaluators.The three settings use synthesis with formal verification, SPICE, and OpenROAD, respectively.
- Prefix architectures: 17% lower delay and 18% lower area than Kogge-Stone were achieved by formally verified 32-bit prefix adders under a placed-and-timed flow.The discovered architectures are absent from the training corpus, and correctness is verified before and after technology mapping.
- Analog amplifier topologies: Conformal-health SMC raised structural validity from 24.2% to 72.3% and Pareto hypervolume from 20.5 to 27.1 under a matched budget.Trajectory information allocates exploration and evaluation effort before expensive simulation.
- Analog amplifier topologies: 57.4 dB was the best raw gain after generation-wise search, rising from 10.8 dB while later generations expanded novelty coverage.The final scored population and nondominated front encode the novelty-gain trade-off.
- Analog amplifier topologies: Seven amplifier topologies absent from the training corpus remained validated after independent resizing and re-simulation.They span gains of 21.9-66.1 dB and bandwidths of 72.9 kHz-207 MHz, with noncanonical reinforcing paths and regenerative feedback.
- Continuous spatial organization: 0.68× the OpenROAD Auto placer's wirelength was reached on held-out macro-placement designs.All 16 zero-shot nvdla samples beat Auto, while mixed-size designs could degrade to 1.07× on bp_quad.
5 Ablations and Analysis
The analysis shows that evaluator-aware pruning and learned mutation are especially valuable when evaluation is costly or representations are structurally fragile. Their necessity varies by design space, with random mutation sometimes remaining viable where decoding preserves validity.
- Are both learned components necessary?: Table 4 compares prior and mutation components at matched budgets, using prefix-adder delay–area hypervolume and placement change in hypervolume.Placement ΔHV is relative to the initial population, and lower OpenROAD routing overflow is better.
- When mid-generation steering helps: 72.3% structural validity and 4.8 simulations per scored candidate result from pruning analog candidates under costly evaluation.Without pruning, structural validity is 24.2% and simulations per scored candidate are 17.1.
- When mid-generation steering helps: 17.1 to 4.8 simulations per scored candidate quantifies pruning’s reduction in expensive analog evaluations.The same intervention raises hypervolume from 20.5 to 27.1.
- When mid-generation steering helps: 192 particles resampled to 7 architectures reduce prefix-adder hypervolume from 67.8 to 53.6, making diversity more important than pruning there.Prefix-adder evaluation takes milliseconds, unlike analog evaluation.
- Are both learned components necessary?: 28 to 0 SPICE-scoreable analog offspring and 5 to 0 Pareto topologies show that random mutation destroys structure required by analog design.Placement returns the seed under random mutation, while prefix adders retain hypervolume because their grid keeps edits decodable.
- Are both learned components necessary?: 0.68× Auto placement, 7 verified analog topologies, and a prefix-adder front expanding from 14 to 22 show evaluator feedback improves discovery outcomes.The analog result spans gains of 36.2 to 66.1 dB.
6 Conclusion
The paper concludes that diffusion models can operate as learned search operators for discovery beyond the training corpus. Across electronic design spaces, feasible-region learning, diffusion transitions, and external evaluation support verified, novel, and competitive artifacts, subject to stated limitations.
- 6 Conclusion: Diffusion models serve as learned search operators that discover artifacts beyond the training corpus.The framework learns both where valid artifacts exist and how they evolve.
- 6 Conclusion: External evaluators remain the authority for feasibility and quality across the three electronic design spaces.The learned distribution supplies a feasible search space, while diffusion dynamics provide artifact-to-artifact transitions.
- 6 Conclusion: The framework discovers formally verified prefix adders, independently simulated unseen amplifier topologies, and competitive placements on unseen designs.These outcomes span delay and area improvement, independent simulation validation, and macro-placement quality.
- 6 Conclusion: Evaluator cost, representation dependence, and policy-specific conformal calibration limit the framework’s scope.These limitations are stated as boundaries of the overall approach.