CAD-WAM: Anticipating Geometry for Text-to-CAD Generation

Zhengyang Li; Weijie Zheng; Yuxin Cui; Sijie Wang; Wenjie Feng; Qiyu Kang

cs.CVOct 29, 2026

CAD-WAM: Anticipating Geometry for Text-to-CAD Generation

Authors: Zhengyang Li, Weijie Zheng, Yuxin Cui, Sijie Wang, Wenjie Feng, Qiyu Kang

Organizations: University of Science and Technology of China · Nanyang Technological University

Abstract

Generating editable computer-aided design (CAD) models from text requires selecting operations that produce the intended changes to the geometry constructed so far. An incorrect operation can compromise subsequent steps, making reliable multi-step generation challenging. Existing methods based on large language models (LLMs) primarily learn to predict commands, without explicit supervision of the geometric states those commands should produce. Inspired by world-action models, we introduce CAD-WAM, which couples geometry-conditioned action generation with next-state prediction. We define complete modeling operations as actions in a CAD domain-specific language (DSL) and encode surface point clouds of intermediate solids into compact latent states using a pretrained variational autoencoder. An LLM backbone generates the next action from the target description and current geometric state, while an auxiliary head on the same backbone predicts the next state to provide geometric supervision during training. We construct step-wise training trajectories from parametric CAD models in the DeepCAD dataset, pairing each trajectory with an expert-level textual description. At inference, each generated action is executed by a CAD kernel, and the resulting solid is re-encoded to inform the next decision. On the DeepCAD test set, CAD-WAM outperforms the task-specific baselines in geometric accuracy and output validity, with larger gains on models requiring more operations, and produces more accurate geometry than general-purpose LLMs prompted with the same DSL. Ablations further show that next-state supervision reduces mean Chamfer distance by 13.2% relative to an otherwise identical model trained only to predict actions. Code is available at https://github.com/Lzy-1037/CAD-WAM.

Figures & tables

Figure 1: Our CAD DSL. Top: a construction sequence in which every action yields a valid solid. Bottom left: an action serialized as a JSON object. Bottom right: execution of an action, whose parameters are validated before the CAD kernel is invoked.

Figure 2: Architecture of CAD-WAM: the Geometric State Embedding maps the geometric state to 16 geometric tokens that follow the textual tokens in the backbone; the Action Head generates the next action and the State Prediction Head regresses the next geometric state.

Figure 3: Overview of CAD-WAM, which builds the model step by step, executing each predicted action and re-encoding the resulting solid.

Metric	Text2 CAD	CAD- Coder	CADFS- 8B	Pointer- CAD	cadrille (text)	CAD- WAM (Ours)	Qwen3.8- Flash	DeepSeek V4.1- Flash	GPT-6 Astra	Claude Opus 5.5
IR (%) $\downarrow$	2.627	0.741	8.125	8.800	2.529	0.666	28.360	29.478	0.025	9.068
CD $\downarrow$ mean median	12.896	3.292	4.151	2.580	3.391	1.142	3.717	3.158	1.755	3.106
	0.554	0.210	0.196	0.300	0.218	0.166	0.206	0.200	0.173	0.197
HD $\downarrow$ mean median	14.446	6.576	7.491	–	7.365	4.134	6.634	6.304	4.728	6.354
	5.687	3.089	3.038	–	3.166	2.783	3.053	3.029	2.841	3.020
NC $\uparrow$ mean median	0.693	0.845	0.839	–	0.836	0.903	0.854	0.860	0.888	0.859

Table 1: Quantitative comparison with existing CAD generation methods and general-purpose large language models.

Figure 4: Per-model results for all compared systems. (a) Cumulative distribution of the Chamfer distance over the attempted models. (b) Quartile boxes with p5–p95 whiskers, ordered by median. (c) Mean Chamfer distance by number of actions. (d) Invalidity ratio by number of actions. Pointer-CAD is omitted, as its predictions are not accessible to us.

State	IR (%) $\downarrow$	CD $\downarrow$		HD $\downarrow$		NC $\uparrow$		ECD $\downarrow$	IoU $\uparrow$	Euler match (%) $\uparrow$
State	IR (%) $\downarrow$	mean	median	mean	median	mean	median	ECD $\downarrow$	IoU $\uparrow$	Euler match (%) $\uparrow$
Latent State	0.666	1.142	0.166	4.134	2.783	0.903	0.964	7.313	0.964	95.850
Text State	1.482	1.405	0.172	4.619	2.834	0.893	0.964	7.996	0.952	94.556

Table 2: Comparison between latent geometric states and textual states.

Configuration	IR (%) $\downarrow$	CD $\downarrow$		HD $\downarrow$		NC $\uparrow$		ECD $\downarrow$	IoU $\uparrow$	Euler match (%) $\uparrow$
Configuration	IR (%) $\downarrow$	mean	median	mean	median	mean	median	ECD $\downarrow$	IoU $\uparrow$	Euler match (%) $\uparrow$
w/o State Prediction Head	0.779	1.316	0.167	4.264	2.785	0.902	0.964	7.374	0.960	95.404
w/ State Prediction Head	0.666	1.142	0.166	4.134	2.783	0.903	0.964	7.313	0.964	95.850

Table 3: Ablation study on the State Prediction Head.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Field	Type	Meaning
kind	string	operation identifier, "extrude"
plane.origin	3 floats	origin of the sketch plane
plane.normal	3 floats	plane normal, along which the profile is extruded
plane.x_dir	3 floats	in-plane $x$ direction
profile.loops	list	closed loops of lines, arcs and circles
forward	float $\geq 0$	extrusion distance along the normal

Appendix

Table 4: Fields of an extrusion action.

Panel of Figure 5 — Figure 5: An action of our DSL. A square profile with one rounded corner is drawn on the $xy$ -plane and extruded as a new body.

Figure 6: SetVAE pretraining. Left: training and validation Chamfer distance per epoch on a logarithmic scale, with the selected checkpoint marked. Right: the Kullback-Leibler term and its weight schedule.

Figure 7: Reconstructions of test-split solids that the encoder never observed during pretraining, including intermediate solids from several construction steps. Input clouds are shown above their reconstructions.

Architecture
Backbone	Qwen2.5-1.5B-Instruct
Geometric tokens	16
Slot width	256
Geometric State Embedding	2 Transformer layers, 8 heads, feed-forward width 1024
State Prediction Head	mean pooling, LayerNorm, MLP $d\rightarrow 2048\rightarrow 1024$ (GELU)
Added parameters	11.4M, or 0.74% of the backbone

Appendix

Table 5: Configuration of CAD-WAM.

	Models	Records
DeepCAD models	178,238
Geometrically verified	176,226
With an expert description	174,582	526,010
Training split	157,945	475,656
Validation split	8,755	26,394
Test split	7,882	23,960

Appendix

Table 6: Construction of the step-wise dataset. The test split lists the models for which step-wise records exist, whereas the evaluation set comprises all test models that carry a description, including 80 models that do not pass verification.

Figure 8: Statistics of the step-wise dataset. Left: number of actions per model, shown as a share of the training and of the test split on a logarithmic scale. Middle: composition of the sketch profiles by curve type. Right: distribution of the Boolean operations over all actions.

Panel of Figure 9 — Figure 9: A record of the step-wise dataset, taken from the test split. The input contains the instruction, the description of the target model, the progress information and the geometric state of the current solid; the description is shortened here. The target is the next action, which cuts a ring into the bracket. The supervision also includes the geometric state of the solid that this action produces.

System	Outputs	Generation	Attempted
Text2CAD	our inference	single pass	7,841
CAD-Coder	our inference	single pass	7,958
cadrille	our inference	single pass	7,949
CADFS	released results	single pass	7,212
Pointer-CAD	published results	step-wise	–
Qwen3.8-Flash	API	DSL, rendered views	7,962

Appendix

Table 7: Configuration of the compared systems. ”Attempted” is the number of test models the system was run on.

Figure 10: Textual state of an intermediate solid and the solid it describes. The part is a block with a cylindrical through-hole, which the state reports as six planar faces and one concave cylindrical face; three of the seven faces are shown.

Metric	$\lambda=0$	$\lambda=0.01$	$\lambda=0.03$	$\lambda=0.05$	$\lambda=0.1$
IR (%) $\downarrow$	0.779	0.691	0.666	0.791	0.804
CD $\downarrow$	1.316	1.229	1.142	1.232	1.107
HD $\downarrow$	4.264	4.203	4.134	4.163	4.184
NC $\uparrow$	0.902	0.902	0.903	0.903	0.903
ECD $\downarrow$	7.374	7.251	7.313	7.189	7.196
IoU $\uparrow$	0.960	0.961	0.964	0.963	0.962

Appendix

Table 8: Ablation study on the state prediction loss weight

\lambda

. CD, HD, and NC are reported as mean values.

Figure 11: Predictions of each system on six test models, ordered by the number of construction steps of the reference. invalid marks a prediction that does not build a valid solid.

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