Test-Time Scaling for CAD Generation via Verifier-Free Consensus Selection

arXiv: 2608.09706v1 [cs.CE], 10 Aug 2026

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Large language models can write parametric CAD programs from natural-language descriptions (text-to-CAD generation), but a single sample is often wrong: dimensions are inaccurate, features are missing, or the compiled shape does not match the prompt. A common mitigation strategy is to sample multiple candidates and select the most viable one. The open question is how to pick when there is no ground-truth model, no learned reward model, and no feedback loop that judges each candidate.

Existing systems often require a separate verifier, such as a vision-language judge, to select among candidates. However, such judges add model calls and can exhibit self-preference, weak discrimination, over-optimization, or gaming. The authors investigate whether the candidate pool itself provides enough signal for effective selection, offering a verifier-free alternative.

The authors introduce consensus selection: sample N parametric CAD programs from an LLM, compile them to 3D models, and return the candidate that agrees most with the rest of the pool. The method is training-free and compatible with existing CAD agents.

Formally, for a distance function d, the method selects the model with the lowest average distance to all others:

i* = arg min (1/(V-1)) Σ j∈Vi d(S i, S j)

This is mathematically equivalent to minimum Bayes risk (MBR) decoding with d as the loss function and a uniform distribution over the sampled candidates.

1. Geometric consensus: For each model, sample a point cloud uniformly from its surface; normalize and align pairs with ICP; measure agreement via symmetric Chamfer distance between point clouds. This picks the geometrically most central model of the pool.

2. Topological consensus: Compare candidates by Euler characteristic χ(S) of the mesh (vertices minus edges plus faces; defined for watertight meshes). The topological distance is 0 if χ(S i) = χ(S j), 1 otherwise. This selects the candidate from the largest group of models with identical topology. Ties are broken by geometric consensus.

• Training-free and model-agnostic

• Requires only a compiler and O(V2) pairwise distance evaluations

• Makes no assumption about how the candidate pool was generated

• Can be applied on top of any existing generation pipeline

Benchmark: CADPrompt benchmark (200 natural-language descriptions of CAD objects with ground-truth models), each in two variants: with and without explicit measurements.

Candidate generation: Few-shot setup of EvoCAD: LLM receives a short CadQuery introduction, five example programs drawn at random from EvoCAD's pool of 40 few-shot examples, and the object description; sampling uses temperature 0.5; candidates that fail to compile are discarded without repair.

Metrics: Chamfer distance (CD), 95th-percentile Hausdorff distance (HDD), voxel IoU, absolute error in Euler characteristic (T err), percentage of correct topologies (T corr), and coverage (percentage of prompts yielding at least one successfully compiled candidate).

Using the exact same initial EvoCAD candidate pools (six candidates per prompt), consensus selection was compared against the EvoCAD verifier:

• Geometry: Both consensus variants improve all geometric metrics over verifier selection from the same candidate pool. Geometric consensus improves CD, HDD, and IoU over the verifier (all p ≤ 0.022). Topological consensus significantly improves CD and IoU over verifier-based selection (p = 0.003 and p = 0.035). Both consensus variants also obtain lower CD and higher IoU than full evolution.

• Topology: Topological consensus improves over random selection (T err from 0.542 to 0.465; T corr from 82.1% to 84.9%). No significant topology difference between topological consensus and verifier-based selection (p = 0.82 for T err and p = 1.00 for T corr).

Using gpt-oss-20b pools on prompts without explicit measurements (182 prompts for geometry, 180 for topology):

• Both consensus variants improve over random selection already at N=3 and saturate quickly, with little additional gain beyond N≈9.

• The oracle keeps improving as candidate pools contain better models than any agreement-based selection recovers.

• The choice of selection criteria determines which metric improves: geometric consensus performs best in Chamfer distance for every N, while topological consensus achieves the highest T corr.

Applied geometric consensus to candidate pools of four models (Gemma 3 12B, gpt-oss-20b, Gemma 4, Gemini 3 Flash), each with both prompt variants, generating 30 candidates per prompt and evaluating at N=15 with 1000 random subsets per prompt:

• Consensus selection improves over random selection for every model and both prompt variants.

• Relative CD improvement is 8–10% for Gemma 3 12B and gpt-oss-20b, and only 1–3% for Gemini 3 Flash and Gemma 4.

• Stronger models produce better random picks.

• Prompts with explicit measurements generally lead to better geometry, albeit at slightly lower coverage.

• The oracle remains clearly better than the consensus candidate in all settings.

• Consensus selection and the verifier select from identical candidate pools in Section 4.2, so differences come only from the selection rule.

• On topology, the Euler characteristic may be too coarse to provide a strong consensus signal.

• Consensus cannot help when all candidates are identical.

• Consensus can fail when the same error appears in most candidates, because that error becomes part of the consensus.

• Consensus favors candidates near the center of the pool and may miss a high-quality outlier, helping explain the gap to the oracle.

• Geometric consensus normalizes and aligns models before comparison, so absolute dimensions do not affect selection even when specified in the prompt.

• Small local features may be hard to distinguish with a global distance.

• Future work could compare candidates at the feature or region level, use other criteria (dimensions, manufacturability, engineering simulations), create new CAD models from shared features, or explore consensus across sequential refinements.

The authors introduced and comprehensively evaluated 3D CAD consensus selection for parametric CAD generation. On the exact candidate pools of a state-of-the-art verifier-based agent, geometric consensus improves all evaluated geometry metrics over the verifier. Regarding topology, no significant difference was found between topological consensus and the verifier. Across all tested models and prompt variants, geometric consensus improves over random selection. The method is training-free and can be integrated into existing CAD generation pipelines. The authors conclude that CAD verifiers used for candidate selection should therefore be compared against consensus selection on the same candidate pool.

Improvement 1: Verifier-Free Candidate Selection for Generative Design Systems

The improved AI system can select the most reliable output from multiple generated candidates without needing a separate reward model, learned verifier, or vision-language judge. By computing pairwise geometric consensus (via Chamfer distance after ICP alignment) or topological consensus (via Euler characteristic) across the candidate pool, the system automatically picks the most representative solution. This reduces computational overhead, avoids verifier biases (e.g., self-preference, gaming), and works in domains where ground truth is unavailable—such as CAD, architecture, or 3D printing—enabling robust design generation with only a compiler and distance function.

Improvement 2: Topology-Aware Quality Control for Parametric Modeling

The improved system can detect and prioritize topological correctness in generated 3D models by grouping candidates with identical Euler characteristics and selecting from the largest group. This ensures the output maintains structural integrity (e.g., watertight meshes, correct hole counts) even when geometric details vary. It can be used as a post-processing filter in CAD pipelines to reject candidates with broken topology, improving downstream manufacturability and simulation readiness without additional training.

Improvement 3: Scalable Consensus Scoring for Multi-Model Ensembles

The improved system can aggregate outputs from multiple LLMs (e.g., Gemma, GPT, Gemini) by applying consensus selection to their combined candidate pools. It ranks candidates by average pairwise distance, allowing the system to leverage diverse model strengths while filtering out idiosyncratic errors. This yields consistent quality improvements (8–10% relative Chamfer distance reduction for weaker models) and can be tuned to favor specific metrics (e.g., geometric consensus for shape accuracy, topological consensus for structural correctness) based on task requirements.

Improvement 4: Training-Free Adaptive Sampling with Early Stopping

The improved system can dynamically decide how many candidates to sample by monitoring consensus saturation. Since improvements plateau around N=9 candidates, the system can stop sampling early when consensus scores stabilize, saving inference time and compute. This is particularly useful for real-time design tools or resource-constrained environments, where the system balances quality and latency by generating only as many candidates as needed to reach a reliable consensus.

Improvement 5: Outlier-Resilient Selection with Hybrid Consensus

The improved system can mitigate the risk of selecting a low-quality outlier by combining geometric and topological consensus: first, it filters candidates using topological agreement to ensure structural plausibility, then applies geometric consensus to pick the most central shape among the survivors. This hybrid approach reduces the chance of choosing a geometrically central but topologically broken model, improving robustness in complex design tasks where both shape and structure matter.

Improved AI System Capabilities:

• Autonomous CAD generation: Produces accurate, manufacturable 3D models from text prompts without human verification or external judges.

• Multi-model orchestration: Integrates outputs from various LLMs and selects the best consensus candidate, improving reliability in heterogeneous AI pipelines.

• Resource-efficient design: Dynamically adjusts sampling size based on consensus convergence, reducing compute costs while maintaining quality.

• Domain-adaptive selection: Switches between geometric and topological criteria depending on whether precision (e.g., mechanical parts) or structural correctness (e.g., architectural shells) is prioritized.

• Offline batch processing: Applies consensus selection to pre-generated candidate pools, enabling post-hoc quality improvement in existing CAD workflows without retraining.