TopoCtrl: Post-Optimization Topology Editing Toward Target Structural Characteristics

Abstract: Topology optimization can generate high-performance structures, but designers often need to revise the resulting topology in ways that reflect fabrication preferences, structural intuition, or downstream design constraints. In particular, they may wish to explicitly control interpretable structural characteristics such as member thickness, characteristic member length, the number of joints, or the number of members connected to a joint. These quantities are often discrete, non-smooth, or only available through a forward evaluation procedure, making them difficult to impose within conventional optimization pipelines. We present TopoCtrl, a post-optimization control framework that repurposes the latent space of a pre-trained topology foundation model for explicit characteristic-guided editing. Given an optimized topology, TopoCtrl encodes it into the latent space of a latent diffusion model, applies partial noising to preserve instance similarity while creating room for modification, and then performs regression-guided denoising toward a prescribed target characteristic. The concept is to train a lightweight regression model on latent representations annotated with evaluated structural characteristics, and to use its gradient as a differentiable guidance signal during reverse diffusion. This avoids the need for characteristic-specific reformulations, hand-derived sensitivities, or iterative optimization. Because the method operates through partial noising of an existing topology latent, it preserves overall structural similarity while still enabling characteristic controls. Across representative control tasks involving both continuous and discrete structural characteristics, TopoCtrl produces target-aligned topology modifications while better preserving structural coherence and design intent than indirect parameter tuning or naive geometric post-processing.

• The paper introduces TopoCtrl, a regression-guided latent diffusion method that partially noises an optimized topology and steers denoising toward target structural characteristics without deriving task-specific sensitivities.
• TopoCtrl achieves 83.84–99.50% best-of-64 target coverage, 79.21–84.93% IoU, and 0.03–0.10% volume-fraction error across joint, member, length, and thickness controls.
• The method expands control beyond filter-radius tuning, but edited designs show higher structural failure rates and require verification, while extreme targets, limited sampling, and heuristic annotations remain important limitations.

Motivation and problem statement

Topology optimization produces high-performance structures, but the optimized result is rarely the end of the design process. Practitioners frequently need to revise an optimized topology to reflect fabrication preferences, structural intuition, or downstream constraints — for example, adjusting member thickness, characteristic member length, joint count, or the number of members incident to a joint. These quantities are often discrete, non-smooth, or available only through a forward evaluation procedure, which makes them difficult to impose within conventional gradient-based optimization pipelines. Existing remedies each fall short in a specific way: reformulating the optimization with characteristic-specific constraints requires hand-derived sensitivities and repeated solves; varying solver parameters such as filter radius provides only indirect and limited variation; and ad hoc geometric post-processing can compromise structural behavior. The paper identifies a concrete gap: no general tool exists for explicit, instance-preserving control over such characteristics given only a forward evaluator.

Method

TopoCtrl is built on the pre-trained OAT latent diffusion foundation model (Nobari et al., 26 Oct 2025), which maps topologies of arbitrary size and aspect ratio into a fixed-resolution structured latent via a neural-field autoencoder whose decoder features are rendered at arbitrary resolution. The pipeline proceeds as follows:

1. Encoding and partial noising: the input topology $T$ is encoded to $z_0 = E(T)$, then partially noised to an intermediate timestep $\tau \ll T$, yielding $z_\tau$. Because $\bar{\alpha}_\tau$ remains non-negligible, the dominant semantic content (coarse load path, global layout) is preserved while leaving room for modification.
2. Regression guidance: four lightweight convolutional regressors (channel sizes 32–256, batch norm, SiLU, strided downsampling) map latents to scalar characteristics: joint count, maximum members per joint, normalized average of the two longest members, and normalized 90th-percentile thickness. Each is trained on 150K filtered OAT samples annotated via medial-axis skeletonization with pruning and junction-merging heuristics, using MSE loss; training takes roughly 3 minutes per regressor.
3. Guided DDIM denoising: at each reverse step, the clean latent $\hat{z}_0$ is estimated from the velocity-parameterized UNet prediction, the control loss $\|f_\psi(\hat{z}_0) - \tilde{y}^\star\|_2^2$ is backpropagated into the latent with strength $\lambda_{\mathrm{ctrl}}=10$, and a deterministic DDIM update is applied on the guided latent.

The key design choice is that guidance operates on the estimated clean latent rather than the noisy one, and that partial noising (30 of 100 total steps) ties sampling to the original instance. This converts a forward generator into a control tool without characteristic-specific reformulations or sensitivity derivations.

Evaluation setup

Experiments use 100 held-out OAT test topologies across 16 target settings spanning the four characteristics, generating 64 stochastic samples per topology-target pair (~0.5 s per sample on an RTX Pro 6000). Results are reported best-of-N, with characteristics re-evaluated from decoded topologies using the identical medial-axis pipeline used for annotation. A benchmark is constructed by rerunning the test set through topology optimization with filter radii varied from 1.5 to 12 across 7 settings. Failure is defined per the OAT protocol as compliance exceeding twice that of the ground-truth topology.

Results

The central quantitative finding is that TopoCtrl reaches substantially broader target coverage than filter-radius tuning while maintaining high instance similarity. At best-of-64:

Task	Coverage (%)	VFE (%)	IoU (%)	Failure rate (%)
Joints	94.82	0.03	82.51	7.40
Member (max per joint)	99.50	0.03	84.93	4.67
Length	83.84	0.03	82.55	7.00
Thickness	85.02	0.10	79.21	16.00

By comparison, the filter-radius benchmark achieves coverage of only 23.89% (joints), 56.00% (member), 43.80% (length), and 16.94% (thickness). Volume-fraction error drops to 0.03–0.10% at best-of-64, and IoU of roughly 79–85% confirms outputs remain close edits of the original instances. Coverage improves monotonically with N: e.g., joints coverage rises from 66.63% at N=2 to 94.82% at N=64, indicating that reliable control currently depends on substantial stochastic sampling.

Two results deserve emphasis. First, TopoCtrl controls discrete quantities — joint count and maximum joint valence — that have no natural gradient-based formulation in continuum topology optimization; related controls exist mainly in truss layout optimization. Second, although the OAT training data was generated with a fixed filter radius (so the dataset contains no systematically varied feature scales), the method still steers thickness and length in both directions, including increasing characteristic length beyond the nominal optimum — a direction classical feature-scale constraints do not target. Accuracy degrades at extreme targets (e.g., 40 joints for initially simple designs), consistent with both data sparsity and distance from the stiffness optimum. A cantilever-beam case study demonstrates successful control of all four characteristics on an out-of-distribution problem configuration.

An important trade-off is acknowledged directly: failure rates are higher than vanilla OAT generation because controlled topologies are intentionally pushed away from the compliance optimum. This is inherent to the task rather than a defect of the method, but it means edited designs require structural verification before use.

Limitations and open questions

The paper concedes several limitations plainly. The four characteristics rely on manually chosen post-processing thresholds (pruning at 10 pixels, junction merging when local thickness exceeds 6 pixels and distance is below 8 pixels) without manual labeling, so the annotation pipeline itself embeds heuristic choices. Regression accuracy is weakest near distribution tails for the discrete quantities, which propagates into control error at extreme targets. Reliance on up to 64 samples per edit limits responsiveness as an interactive tool — the authors note accuracy remains insufficient with fewer samples. Finally, evaluation covers the OAT test set plus a single cantilever example; generalization across the full space of common topology optimization problems has not been established. Open questions include whether other evaluators (hole count, minimum member angle, manufacturability metrics) can be learned reliably enough from latents to serve as guidance signals, and whether the pipeline extends to 3D once a volumetric topology foundation model exists.

Conclusion

TopoCtrl demonstrates that regression-guided partial denoising in the latent space of a pre-trained topology foundation model provides a practical mechanism for explicit, instance-preserving control of structural characteristics — including discrete ones intractable for conventional optimization — achieving up to 99.5% target coverage versus at most 56% for filter-radius tuning, with high IoU to the source design. Its main costs are elevated failure rates relative to unconstrained generation, dependence on best-of-N sampling, and heuristic characteristic annotation. The framework's generality rests on a single assumption worth scrutiny: that any forward-evaluable characteristic can be regressed accurately enough from the foundation model's latent to yield useful gradients during denoising.