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MIRAGE-CAD: Construction-Mediated Multimodal Generation of Executable CAD Programs

Jizong Zhan

arXiv:2608.28669v1cs.CVcs.PLcs.SE

TL;DR

Recovering construction from final geometry is ambiguous, and MIRAGE-CAD addresses this by mapping four input modalities to a shared construction representation and generating executable CAD through a plan interface. Across held-out queries, it achieves build and STEP-export success without retrieval; controlled comparisons separate the value of construction conditioning from textualisation and motivate evaluating validity, fidelity, and parametric behaviour separately.

  • Problem

    The same final geometry can arise from different construction procedures, so an observed shape does not identify a unique feature history.

    Source: §1.1 · p. 2

  • Method

    MIRAGE-CAD maps text, images, point clouds, and STEP/B-Rep inputs to a shared construction representation, then generates an explicit plan and executable Python CAD program.

    Source: §8 · p. 32

  • Results

    Across 2,500 held-out queries per modality, MIRAGE-CAD achieves 55.4–70.0% Build and 52.3–66.2% STEP export without retrieval at inference.

    Source: §8 · p. 32

  • Takeaways & Limitations

    The explicit plan is an inspectable, separately scorable interface, while executable validity, geometric fidelity, and parametric behaviour describe distinct program properties.

    Source: §8 · p. 32

    On 400 Fusion 360 parts, CAD-Recode substantially outperforms both MIRAGE point-cloud pathways in geometric fidelity, though the comparison does not isolate an architectural cause.

    Source: §7.5 · p. 31

Abstract

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Recovering an executable parametric CAD program from an observed object is fundamentally ambiguous, because the same final geometry can result from different construction procedures. We study this problem from four types of input: natural-language descriptions, rendered images, point clouds, and STEP/B-Rep geometry. MIRAGE-CAD maps each input to a shared construction representation and mediates program generation through an explicit construction-plan interface. The resulting Python CAD code is executed by an OpenCASCADE kernel to build the solid and export it as STEP. On 2,500 held-out queries per modality, the system achieves 55.4-70.0% build success and 52.3-66.2% STEP export success without retrieval at inference. Controlled comparisons show that strong reconstruction does not depend on expressing the construction representation as text: a decoder conditioned directly on the continuous representation also reconstructs strongly, while an exposure-matched plan-based decoder shows no detected material loss in per-part geometric fidelity. The explicit plan instead provides a readable and separately measurable intermediate representation whose agreement with the reference construction is informative about downstream execution success. Finally, we show that executable validity, geometric fidelity, and parametric responsiveness can diverge substantially and should therefore be evaluated separately.

1. Introduction

A final CAD shape does not uniquely reveal its construction history, while retrieval is limited to constructions present in its corpus. MIRAGE-CAD studies whether an intermediate construction representation can mediate multimodal generation and be evaluated separately from executable code.

1.1. Shape is not construction

  • Different procedures can produce the same solid yet respond differently to parameter changes, so geometric agreement cannot identify a unique feature history.The paper therefore targets a plausible construction consistent with the observation, not recovery of a unique original history.Source: §1.1 · p. 2

1.2. Retrieval is strong but finite

  • Retrieval reuses only corpus constructions and can yield a valid program that still differs from the observed part in properties such as scale.The paper uses retrieval as a reference rather than the target of query-conditioned generation.Source: §1.2 · p. 3

1.3. Hypothesis and approach

  • The study compares direct query-to-code generation with continuous construction conditioning and explicit textual plans to isolate the value of construction mediation and textualisation.It also includes retrieval-assisted variants and interventions on information supplied to the decoders.Source: §1.3 · p. 3
  • MIRAGE-CAD maps text, images, point clouds, and STEP/B-Rep inputs to a shared Construction IR, then generates a plan and executable Python CAD code.The program is executed by an OpenCASCADE kernel; image queries have no auxiliary observation block, making the plan a strict information bottleneck for that modality.Source: §1.3 · p. 3

1.4. Contributions

  • The contributions include a four-modality generation pipeline that executes without retrieval at inference and a controlled study finding strong reconstruction does not require textualising construction.The explicit plan remains inspectable and separately measurable, with no detected material per-part fidelity loss in the exposure-matched comparison.Source: §1.4 · pp. 4–5
  • The paper evaluates executable validity, geometric fidelity, and parametric behaviour separately, and examines retrieval redundancy and performance boundaries on external parts.It positions MIRAGE-CAD against CAD-Recode on Fusion 360 parts, distinguishing measurable-geometry coverage from geometric fidelity.Source: §1.4 · p. 5

2. Related Work

Prior CAD generation predicts command sequences or executable code, while multimodal systems condition on varied observations and intermediate structures offer an inspectable interface. The paper distinguishes these approaches and argues that sequence agreement, execution, geometry, and parametric behaviour measure different properties.

2.1. Parametric CAD program generation

  • CAD generation predicts command sequences or executable code, while MIRAGE-CAD instead uses construction as an intermediate target before executable CAD code.Command vocabularies constrain syntax but limit operations; executable-code generation offers richer CAD APIs yet introduces syntax, name-resolution, and API failures.Source: §2.1 · pp. 5–6

2.2. Multimodal conditioning and intermediate representations

  • Continuous conditioning preserves dense information but is not directly inspectable, whereas retrieval and explicit intermediate structures offer inspectable context with different constraints.MIRAGE-CAD predicts a shared construction latent to condition a plan decoder, then passes the plan to the code decoder, enabling comparison of continuous and textual construction conditioning.Source: §2.2 · pp. 6–7

2.3. Evaluating generated CAD

  • Sequence disagreement need not imply geometric error, and successful execution establishes kernel admissibility rather than agreement with the target shape.The paper also measures parametric rebuild validity, geometry response to perturbation, and parameter reachability, and checks construction redundancy using external Fusion 360 parts.Source: §2.3 · p. 7
  • Geometric fidelity measures agreement with the target using Chamfer distance, F-score, or volumetric IoU, so CAD evaluation reports geometry alongside validity.Execution and geometry answer distinct questions: a program can run and produce a valid object without matching the target shape.Source: §2.3 · p. 7

3. Problem Formulation

The task is to generate an executable single-part CAD program from exactly one of four query modalities, not to predict geometry directly or fuse modalities. MIRAGE-CAD represents construction explicitly and evaluates execution, geometry, and parameter behaviour as separate properties.

3.1. Inputs and output

  • Each query supplies exactly one modality—text, rendered image, a surface point cloud, or a STEP/B-Rep descriptor—and multimodal fusion is outside the study.The output is an executable Python CAD program; program execution is a partial mapping because some programs fail before producing a valid solid.Source: §3.1 · p. 8

3.2. Construction intermediate representation

  • A Construction IR document contains a header, parameter declarations, an ordered sequence of feature records, and a terminator.Its 44 operation tokens can refer to named parameters symbolically, while implementation details such as imports, helper functions, and control flow remain in the Python program.Source: §3.2 · pp. 8–9

3.3. Task factorisation

  • Generation is factorised into a modality encoder and prior that predict a construction latent, a plan decoder, and a code decoder that produces the executable program.Both decoders can also receive a query-derived observation block; it is empty for images, making the plan a strict information bottleneck for that modality.Source: §3.3 · p. 9

3.4. Evaluation axes

  • Executable validity requires passing five gates: Python parsing, execution, solid construction, kernel validation, and STEP export.Passing these gates establishes executability and exportability, not correctness of the reconstructed geometry.Source: §3.4 · p. 9
  • Geometric fidelity is measured against target geometry with Chamfer distance and F-score, with volumetric IoU additionally used in external evaluation.The measures apply when geometry can be extracted by the relevant evaluator.Source: §3.4 · pp. 9–10
  • Parametric behaviour measures validity after parameter changes, whether geometry changes, and how much geometric numeric content is reachable through declared parameters.Validity and geometry response are tested over finite parameter perturbations; reachability limits the scope to which those results apply.Source: §3.4 · p. 10
  • Validity, fidelity, and parametric behaviour are reported separately because they describe different properties of a generated program.A successful build does not itself establish geometric correctness, and parameter responsiveness is a distinct evaluation axis.Source: §3.4 · pp. 9–10

3.5. Scope and assumptions

  • The study covers single connected solids, uses procedurally generated kernel-validated programs for training, and excludes assemblies, mating constraints, and full 2D sketch-constraint graphs.Because final geometry does not uniquely identify construction history, the target is a plausible construction consistent with the observation.Source: §3.5 · p. 10

4. MIRAGE-CAD

MIRAGE-CAD uses modality-specific encoders and construction priors to generate a construction plan before executable Python CAD code, with shared decoders and kernel execution. Its training stages align modalities to Construction IR, train plan and code generation, and continue on predicted-plan exposure.

4.1. Architecture overview

  • A modality-specific encoder and prior predict a construction latent, which conditions a plan decoder before a code decoder generates Python CAD for OpenCASCADE execution.The shared generation path does not use retrieval at inference; modality-dependent observations provide auxiliary decoder inputs, except that image queries have none.Source: §4.1 · pp. 10–11

4.2.1. Modality encoders

  • Text uses frozen DistilBERT, images use frozen CLIP ViT-B/32, point clouds use PointNet on 1,024 xyz points, and STEP/B-Rep uses kernel-derived descriptors.The point-cloud branch removes absolute metric scale by centering and normalizing by maximum radius; reported STEP results use a 50-dimensional global descriptor because the corpus lacks independent face or edge records.Source: §4.2.1 · pp. 11–12

4.2.2. IR-anchored alignment

  • The four query modalities are aligned to Construction IR as a common anchor using symmetric InfoNCE, rather than aligned directly to one another.The paper treats the star-shaped alignment as a design choice and does not experimentally compare it with full pairwise alignment.Source: §4.2.2 · p. 12

4.2.3. Construction prior

  • At inference, a separate modality prior predicts the construction-space latent because the reference construction is unavailable.Each prior is an independently trained residual MLP followed by L2 normalisation; its objective combines Euclidean, cosine, and contrastive terms with weights of 1.0.Source: §4.2.3 · pp. 12–13

4.3.1. Prefix adapter

  • A prefix adapter converts the continuous predicted construction latent into a query-dependent continuous prefix for the plan decoder.The prefix has no vocabulary-token identity and conditions only the plan decoder; the code decoder receives neither the latent nor its prefix.Source: §4.3.1 · p. 13

4.3.2. Plan decoder

  • The plan decoder receives prefix vectors before token embeddings and generates the Construction IR plan autoregressively from a prompt and observation block.Training loss applies only to target plan tokens, with prefix and prompt positions masked; the prompt does not contain the Construction-IR grammar.Source: §4.3.2 · p. 13

4.4.1. Code decoder

  • A second LoRA adapter over the shared language-model base generates executable Flluma Python code from the plan and available observation block.The code-generation instruction requires a top-level variable named part, which the execution pipeline consumes.Source: §4.4.1 · p. 14

4.4.2. Deterministic repair and execution

  • Three deterministic rewrites correct recurring operation-alias and argument-format errors before programs are evaluated by the kernel.They do not use execution feedback, resample programs, or alter construction beyond predefined rewrites; main experiments use one program per query without geometry-based selection.Source: §4.4.2 · p. 14

5. Experimental Protocol

The protocol evaluates multimodal CAD generation on procedurally generated parts, with held-out, family-held-out, and external settings. It defines paired comparisons, separates validity, geometry, and parametric metrics, and specifies statistical procedures and implementation conditions.

5.1. Data and evaluation splits

  • Experiments use 100,000 procedurally generated parts, with 25,000 training, 2,500 validation, and 2,500 test samples per modality; additional evaluations cover 2,923 family-held-out and 400 external parts.The family-held-out split tests new combinations of known operations but also uses less training data, so it is treated as a structural diagnostic.Source: §5.1 · pp. 15–16

5.2. Experimental conditions

  • Table 3 conditions define pairwise controls rather than a single-factor ablation; B0 removes both the plan block and its construction-conditioned pathway, while B1 feeds the latent directly to code.B1 uses a prefix adapter and does not generate a textual plan.Source: §5.2 · p. 16, Table 3 · p. 16
  • B1a and B2-Pred use matched one-epoch schedules and closely matched inference exposure, but condition the code decoder on continuous latents and generated text, respectively.Evaluated checkpoints use 3,000 and 3,125 updates, respectively.Source: §5.2 · p. 17
  • B2 is the deployed pathway, B3 substitutes a retrieved plan while retaining the plan-to-code interface, and B4 is used only for external point-cloud positioning.Generation is single-shot by default, without geometry-based candidate selection at test time.Source: §5.2 · p. 17

5.3. Evaluation metrics

  • Validity is measured through five sequential gates—parsing, execution, solid building, kernel validation, and STEP export—with each rate using all attempted queries as its denominator.Geometric fidelity uses symmetric Chamfer distance and F-score at 1% of the reference bounding-box diagonal, with 1,024 surface samples per shape.Source: §5.3 · p. 17
  • Parametric tests perturb exposed parameters independently; Rbuild measures five-gate-valid edits, Rresp measures edits that also change geometry, and reachability tracks parameter-controlled numeric arguments.F@1% also has an empirical self-sampling reference, not an upper bound; non-scoreable outputs are assigned zero only in all-input F-score accounting.Source: §5.3 · pp. 17–18
  • Construction diagnostics compare generated and reference constructions using plan and latent cosine, operation-set F1, and operation-sequence LCS, rather than treating these as direct geometry measures.PART and SEED fields are replaced by fixed placeholders before plan-level metrics are computed.Source: §5.3 · p. 18

5.4. Statistical analysis

  • Validity rates use 95% Wilson intervals, paired binary outcomes use exact McNemar tests, and geometry uses sign tests; diagnostic-value analysis uses 500 exposure-matched samples and 10,000 paired bootstrap resamples.AUROC assesses ranking of build and STEP-export success, while Spearman correlation measures association with geometric fidelity.Source: §5.4 · p. 18

6. Results

MIRAGE-CAD’s construction-mediated pathway substantially improves STEP build and export success over direct query-to-code generation. Further experiments separate the roles of continuous construction conditioning, textual plans, and observation channels, while showing that validity, fidelity, and parameter reachability are distinct outcomes.

6.1. RQ1 — What does construction mediation contribute?

  • 70.0% versus 35.4% Build and 66.2% versus 34.6% STEP export favor deployed B2 over B0 on the 2,500-sample STEP test set.Syntax moves in the opposite direction, from 94.5% to 97.6%, so the main effect is reaching a buildable CAD model rather than producing more parseable Python.Source: §6.1 · p. 20, Table 4 · p. 20

6.1.1. Continuous versus textual construction conditioning

  • 86.2% Build and 85.6% STEP export without plan text show strong continuous conditioning; B2-Pred reaches 90.4% Build and 90.0% STEP export.B2-Pred trains on predicted plans, unlike deployed B2; this comparison is not update-matched. Against B1a, no practically material per-part fidelity cost from textualisation was detected, but the single-seed comparison does not establish general equivalence or a stable coverage advantage.Source: §6.1.1 · pp. 20–22, Table 5 · p. 21

6.1.2. Diagnostic value of the explicit plan

  • Op-Set F1 and Op-Seq LCS reach about 0.73 AUROC for Build and STEP export, versus about 0.48 for scalar latent cosine.Plan metrics correlate with scale-normalised F@1 but are essentially unrelated to raw Chamfer; they compare against one reference construction, and low agreement alone does not imply an incorrect shape. The reference-dependent diagnostics are for offline evaluation, not deployment-time confidence.Source: §6.1.2 · pp. 22–23, Table 6 · p. 22, Figure 3 · p. 23

6.2. RQ2 — What information do the construction and observation channels carry?

  • Construction prefixes carry sample-specific construction information, while observation channels supply additional query evidence, including absolute metric scale where available.Shuffling the prefix lowers plan cosine from 0.886 to 0.047 and Op-Set F1 from 88.0% to 34.6%, yet Build changes only from 71.4% to 68.6% as median Chamfer rises from 2.84 to 22.11 mm2. Suppressing observation reduces STEP’s within-10%-of-target-size rate from 95.3% to 6.6%; this inference-only intervention uses models trained with observation present.Source: §6.2 · pp. 23–25

6.3. RQ3 — Can one shared pipeline serve four modalities?

  • One shared plan decoder and one shared code decoder achieve 55.4–70.0% Build and 52.3–66.2% STEP export across four modalities, with 2,500 queries per modality.Continuing Stage 3 training from STEP latents to a four-modality mixture raises average Build from 42.9% to 60.1%, while STEP decreases by 4.4 points; the table supports a multimodal-system claim, not a modality ranking.Source: §6.3 · pp. 25–26, Table 7 · p. 25

6.4.1. Construction redundancy and the coverage–fidelity trade-off

  • On 1,330 jointly scoreable family-held-out parts, generation’s median F@1 is 0.162 versus retrieval’s 0.111; across all 2,923 parts, mean F@1 reverses to 0.066 versus 0.099.Retrieval has greater coverage, while generation is more faithful among jointly scoreable parts. The nearest retrieved plan has median operation-set F1 of 1.0, so this split is a structural diagnostic, not a construction-held-out benchmark.Source: §6.4.1 · p. 26, Figure 5 · p. 28

6.4.2. External positioning against CAD-Recode

  • On 400 Fusion 360 parts, CAD-Recode measures geometry for 392 versus MIRAGE’s 226; on 369 jointly IoU-scoreable parts, paired medians are 0.9426 versus 0.1621.Retrieval matches CAD-Recode’s measurable-geometry coverage but not its fidelity; this marks a boundary for the current point-cloud pathway on externally authored parts, not a test of continuous versus textual construction.Source: §6.4.2 · p. 27, Table 8 · p. 27, Figure 5 · p. 28

6.5. RQ5 — Are the generated programs parametrically responsive?

  • Of 1,608 parameter perturbations, 1,604 (99.8%) remain five-gate valid and 1,321 (82.2%) produce detectable geometric change.Mean per-part parameter reachability is 29.3%, so fewer than one third of geometric numeric arguments are controlled through declared parameters on average; the main limitation is parameter exposure, not edit stability.Source: §6.5 · pp. 28–29, Table 9 · p. 28

7. Discussion and Limitations

The experiments distinguish the value of construction conditioning from textualising it, and show that execution, geometric fidelity, and parameter responsiveness are separate properties. Their conclusions are bounded by non-identifiable construction histories, procedural redundancy, and limitations in the tested data and pathways.

7.1. Construction representation and textual mediation

  • Removing construction conditioning causes large losses in Build and STEP export, while direct continuous-latent conditioning reconstructs strongly without a textual plan.In the exposure-matched STEP comparison, no practically material per-part fidelity difference was detected; the single-seed, slightly update-mismatched test is not a general equivalence result.Source: §7.1 · p. 29
  • The plan is a readable, separately scorable interface whose agreement with reference construction predicts Build and STEP-export outcomes better than latent cosine, while the observation block carries scale information.Plan diagnostics reach AUROC values around 0.70–0.73, but require reference constructions; the observation-block finding is specific to an inference-time intervention on a model trained with that block.Source: §7.1 · p. 29

7.2. Validity, fidelity, and parametric behaviour

  • A program can build successfully despite poor geometry, and responsive exposed parameters still reach only 29.3% of geometric numeric arguments on average.The authors therefore treat validity, fidelity, and parametric behaviour as distinct evaluation targets.Source: §7.2 · p. 30

7.3. Non-identifiability of construction histories

  • Because one solid can arise from different histories, plan metrics measure agreement with a reference rather than unique construction accuracy; evaluating against multiple valid histories remains open.A reference-based metric may penalise an alternative construction that yields equally valid geometry.Source: §7.3 · p. 30

7.4. Procedural redundancy and benchmark design

  • Family-held-out retrieval remains extremely strong, with median operation-set F1 of 1.0, because different template families can share construction skeletons.The authors argue that compositional-generalisation benchmarks should separate examples in construction space, not only by generator-defined family.Source: §7.4 · p. 31

7.5. Limitations

  • The continuous-versus-textual comparison uses one checkpoint per condition, measures test-part rather than training-seed variation, and differs slightly in optimisation budget.The small Build advantage of the textual arm is not an established general effect.Source: §7.5 · p. 31
  • On 400 external Fusion 360 parts, CAD-Recode substantially outperforms both MIRAGE point-cloud pathways in geometric fidelity, but the differing systems do not isolate an architectural cause.The comparison establishes a practical boundary for the current point-cloud pathway, not a general claim about point clouds.Source: §7.5 · p. 31
  • The procedural corpus has plausible but unobserved histories and measured redundancy; encoder capacities differ, point-cloud preprocessing removes scale, and parameter reachability and single-part scope remain limited.Fewer than one third of geometric numeric arguments are reachable through declared parameters; assemblies, mating constraints, and full sketch-constraint graphs are outside scope.Source: §7.5 · pp. 31–32

8. Conclusion

MIRAGE-CAD generates executable CAD programs from four input modalities through a shared construction representation, with an explicit plan interface. Its results separate the roles of construction conditioning and textualisation, while highlighting distinct evaluation axes and limits in the current point-cloud pathway.

8. Conclusion

  • Across 2,500 held-out queries per modality, MIRAGE-CAD reaches 55.4–70.0% Build and 52.3–66.2% STEP export without retrieval at inference.The system generates Python CAD programs from text, rendered images, point clouds, and STEP/B-Rep observations.Source: §8 · p. 32
  • Strong reconstruction does not require textualising the construction representation; the explicit plan instead provides an inspectable, separately scorable interface.Under tested exposure-matched STEP conditions, no practically material per-part fidelity cost was detected for the textual interface relative to direct continuous conditioning.Source: §8 · p. 32
  • Executable validity, geometric fidelity, and parametric behaviour diverge, while procedural redundancy and the current point-cloud pathway bound the conclusions.The paper calls for evaluation methods that account for the non-identifiability of valid CAD construction histories.Source: §8 · pp. 32–33

Code and data availability

The paper releases its training and evaluation code, Construction IR tooling, and validation scripts, while distributing the corpus separately under its original terms. Its appendices specify the IR grammar and operation inventory and clarify that STEP input in this corpus carries sample-specific information primarily through global statistics.

Code and data availability

  • The code, Construction IR tooling, and quantitative-validation scripts are public; the corpus and CAD-Recode checkpoint are not redistributed in the repository.The corpus is distributed separately under its original terms, and the checkpoint is loaded from its upstream release.Source: Code and data availability · p. 33

Appendix A.1. Statement grammar

  • Across 25,000 STEP-modality training samples, the Construction IR contains 25,000 PART, 175,141 PARAM, 137,018 F, and 25,000 END statements.Feature records can include dependencies and targets, and feature arguments can reference declared parameters by name.Source: Appendix A.1 · pp. 33–34

Appendix A.2. Semantic and role vocabularies

  • The IR uses 44 operation tokens, 118 SEM values, and seven ROLE values; operation-level metrics use OP_* identifiers, not SEM or ROLE.SEM is treated as an open semantic vocabulary rather than a fixed categorical set.Source: Appendix A.3 · p. 34, Appendix A.2 · p. 34

Appendix A.4. Operation-frequency distribution

  • OP_HOLE_PATTERN appears in 88.4% of training samples, while 23 of 44 operations occur in fewer than 2%, so aggregate Op-Set F1 can understate rare-operation weaknesses.The operation inventory's document coverage counts samples containing an operation, not total operation occurrences.Source: Appendix A.3 · p. 34, Table A.1 · p. 35, Appendix A.4 · p. 36

Appendix B.2. Effective input in the present corpus

  • Although the STEP/B-Rep encoder accepts global, face, edge, and relation streams, only its 50-dimensional global descriptor varies across samples in this corpus.The face and edge streams are fully masked and the relation stream is constant; the STEP results therefore do not evaluate detailed topology-aware input.Source: Appendix B.1 · p. 36, Appendix B.2 · pp. 36–37

Appendix B.4. Absolute-scale information

  • The STEP descriptor retains absolute metric scale through bounding-box extents, surface area, and volume, whereas point-cloud preprocessing removes absolute size by dividing by maximum radius.The point-cloud scale behavior is a property of the current preprocessing, not an intrinsic limitation of point clouds.Source: Appendix B.4 · p. 37, Table B.1 · p. 38

Appendix C.1. Direct-latent training sensitivity and practical-effect analysis

These diagnostics show that training exposure and optimization affect output coverage and program behavior, while the measured effects on per-part fidelity can be smaller or statistically undetected. Cross-modal and predicted-plan continuation improve some deployed conditions, but do not remove all mismatches.

Appendix C.1. Direct-latent training sensitivity and practical-effect analysis

  • Increasing B1 training from 3,000 to 9,000 updates raises Build from 86.2% to 93.6% and exported parts from 428 to 468, while median Chamfer falls from 2.293 to 2.222 mm2 on 398 jointly scoreable parts.The additional optimization affects coverage more than per-part geometric fidelity.Source: Appendix C.1 · pp. 38–39
  • For the one-epoch B1a–B2-Pred comparison, the paired fidelity test establishes no direction (182:211, p = 0.158), and the estimated Chamfer and F@1 intervals include zero within empirical margins.The comparison is single-seed, has checkpoint-selection and decoder-interface asymmetries, and does not establish general equivalence.Source: Appendix C.1 · pp. 39–40

Appendix C.2.1. Stage 3b: cross-modal continuation

  • Four-modality continuation raises average Build from 42.9% to 60.1%; the three non-STEP modalities gain 18.9–28.7 points while STEP falls 4.4 points.This indicates sensitivity to the latent distribution used to train the shared plan decoder, not equivalent information across modalities.Source: Table C.1 · p. 40, Appendix C.2.1 · pp. 40–41

Appendix C.2.2. Stage 4b: predicted-plan continuation

  • On the 500-row controlled evaluation, Stage 4b raises predicted-plan Build from 28% to 67%, while reference-plan Build decreases from 95% to 89%.Training entirely on predicted plans reaches 90.4% Build; the 70/30 continuation reduces but does not remove the plan-exposure mismatch.Source: Appendix C.2.2 · p. 41

Appendix C.3. Construction-anchor analysis

  • Six oversampled operation families show 80–92% failure rates, alongside high pairwise Construction-IR embedding similarity before modality alignment.The analysis identifies the shared construction anchor as one source of difficulty but does not isolate which part of its pipeline is responsible.Source: Appendix C.3 · pp. 41–42

Appendix D. Observation-Channel and Prefix Interventions

  • Shuffling the prefix reduces plan cosine from 0.886 to 0.047 and Op-Set F1 from 88.0% to 34.6%; the shuffled condition is also below zero-prefix Op-Set F1 of 38.1%.Using the reference-plan latent yields plan cosine 0.898 and Op-Set F1 88.7%, with no detected difference from the deployed prior (p = 0.26).Source: Appendix D · p. 43, Table D.1 · p. 43
  • Removing the observation block lowers STEP Build from 71.4% to 58.0%, while text Build changes from 59.6% to 58.0%; geometry worsens substantially in both modalities.These inference-time suppressions are not retrained architectures, and their results reflect distribution shift as well as information removal.Source: Appendix D · p. 44, Table D.2 · p. 44

Appendix D.2. Absolute-scale analysis

Observation-channel interventions show that the channel is a major source of absolute-scale information for the tested deployed decoders, while Build can remain similar even as geometry deteriorates. The image-path null control confirms that suppression is inert when that channel is empty.

Appendix D.2. Absolute-scale analysis

  • With the observation block present, median bounding-box ratio is 1.000 in all three comparisons and 84.5–95.3% of parts lie within 10% of target size; after suppression, the ratio is 0.609–0.645 and the rate is 6.5–10.1%.For these deployed decoders, the observation channel is the dominant source of absolute metric-scale information in the tested conditions.Source: Appendix D.2 · p. 45
  • STEP leads text by 11.8 Build points with observations, but both reach 58.0% after suppression; geometry deteriorates strongly in both modalities.The intervention measures dependence of deployed checkpoints on the channel, not performance of architectures retrained without it.Source: Appendix D.2 · p. 46, Appendix D.4 · pp. 46–47
  • Chamfer and F@1 order the plan-only and shuffled-with-observation conditions oppositely: median CD is 49.28 versus 22.08, while median F@1 is 0.051 versus 0.027.Chamfer responds to absolute scale, whereas the F@1 threshold is normalized by the reference bounding-box diagonal.Source: Appendix D.2 · p. 46

Appendix D.3. Image-path null control

  • All 500 image samples produce byte-identical programs with and without suppression, while STEP and text comparisons are identical for 0 of 500 samples.The null control confirms that suppression is inert when the image observation field is empty.Source: Appendix D.3 · p. 46

Appendix D.4. Scope of the intervention

  • Geometric comparisons are conditional on joint metric scoreability, so their denominators are smaller than the all-input Build denominators, especially in the crossed suppression cell.The appendix reports coverage separately from conditional fidelity and does not generalize the selective crossed-cell result to all inputs.Source: Appendix D.4 · p. 47

Appendix E.1. Full family-held-out results

Family-held-out evaluation retains a large Build advantage for retrieval, consistent with cross-family reuse of operation skeletons rather than construction novelty. The appendix also separates conditional fidelity from coverage and documents the scope and resolution of the external CAD-Recode comparison.

Appendix E.1. Full family-held-out results

  • On 2,923 held-out-family samples, retrieval remains at 97.6–100.0% Build, while the generated pathway ranges from 45.0% to 62.4%.The family-held-out split is a structural diagnostic; it does not remove construction patterns exploited by nearest-neighbour retrieval.Source: Table E.1 · p. 47, Appendix E.1 · p. 47

Appendix E.2. Construction-skeleton redundancy

  • The nearest retrieved neighbour has median operation-set F1 of exactly 1.0 against the reference plan, showing that held-out queries often share operation sets with training samples from other families.Family identity and construction structure are not equivalent, so family-based separation alone is insufficient as a proxy for construction novelty.Source: Appendix E.2 · p. 48

Appendix E.3. Coverage and conditional fidelity

  • For family-held-out STEP, generation has higher median F@1 and wins 982 of 1,329 non-tied jointly scoreable comparisons, but retrieval leads when all inputs are counted because it produces scoreable geometry more often.This is a coverage–fidelity trade-off; the passage identifies the pattern as specific to STEP, while point-cloud conditional F@1 is 0.022 for generation and 0.020 for retrieval.Source: Appendix E.3 · pp. 48–49, Table E.2 · p. 48

Appendix E.4. Survivorship analysis

  • Among retrieval-scoreable parts, retrieval's median F@1 differs by 0.0068 between jointly scoreable parts and parts not scoreable by generation, about 14% of the conditional generation–retrieval gap.The jointly scoreable subset is somewhat easier for retrieval, but this shift captures only one aspect of selection.Source: Appendix E.4 · p. 49

Appendix F.1. Information conditions and common evaluator

  • The external comparison is system-level positioning under a common evaluator, not a reproduction of CAD-Recode's published benchmark; both prediction and reference are normalized to the unit cube, removing absolute scale.The point inputs also differ in preprocessing and point count, which the comparison does not equalize.Source: Appendix F.1 · pp. 49–51

Appendix F.2. Tessellation and convergence

  • A ten-times-finer tessellation yields median absolute IoU deviation 2.5 × 10^-5 and 95th-percentile deviation 3.7 × 10^-4, smaller than the observed between-system IoU differences.No paired Chamfer difference falls below the part-pair sampling-resolution threshold in either the generated-plan or Prior-NN-IR comparison.Source: Appendix F.2 · p. 51, Appendix F.3 · p. 51

Appendix F.3. Sampling-resolution analysis

  • Relative to each part's sampling floor, CAD-Recode's median Chamfer ratio is approximately 1.24–1.29, while the MIRAGE pathways are 208 and 782 times above their corresponding floors.Together with the IoU ordering, these checks indicate that finite sampling resolution does not explain the external fidelity gap.Source: Appendix F.3 · p. 51

Appendix F.4. Metric scoreability and failure breakdown

The point-cloud comparison shows substantially lower fidelity for the generated-plan pathway than CAD-Recode, even among measurable outputs. The appendix also distinguishes metric scoreability from execution validity and documents the evaluation setup and run limitations.

Appendix F.4. Metric scoreability and failure breakdown

  • Of 400 generated-plan inputs, 174 do not reach measurable geometry; nine MIRAGE outputs pass all five internal validity gates but remain unscoreable externally.The generated-plan pathway exports 232 STEP files, of which 226 are measurable; Boolean failures affect 14 of those measurable outputs and affect IoU but not CD.Source: Appendix F.4 · pp. 51–52
  • The 226 measurable generated-plan outputs still have substantially lower fidelity than CAD-Recode, and the comparison concerns system-level point-cloud reconstruction.The authors distinguish this comparison from experiments on the internal construction representation.Source: Appendix F.4 · p. 52, Appendix F.5 · p. 53

Appendix F.5. Additional paired statistics

  • On 369 jointly IoU-scoreable parts, median IoU is 0.1621 for Prior-NN-IR and 0.9426 for CAD-Recode, despite equal marginal measurable-geometry coverage.The paired medians differ from marginal medians because the scoreable subsets are not identical; CAD-Recode's median CD is 0.117 on parts jointly scoreable with the generated-plan arm versus 0.186 across its 392 CD-scoreable parts.Source: Appendix F.5 · pp. 52–53

Appendix G.1. Corpus composition and splits

  • The corpus uses four complexity tiers, with 25,000 training, 2,500 validation, and 2,500 test samples per modality; retrieval indices use training samples only.Reference programs are executed and kernel-validated during corpus construction, so reported evaluation failures arise from generated programs.Source: Appendix G.1 · p. 53

Appendix G.2. Hardware and quantisation

  • Experiments ran on one 16 GB RTX 5060 Ti, with QLoRA-quantised language-model stages and sequential adapter loading to fit inference in GPU memory.The language-model stages use Qwen2.5-Coder-1.5B with 4-bit NF4 weights; smaller encoders and MLPs train in bfloat16 without 4-bit quantisation.Source: Appendix G.2 · pp. 53–54

Appendix G.3. Per-stage training settings

  • Training proceeds through alignment, latent-prior fitting, plan and code decoder training, and predicted-plan continuation, while controlled decoder comparisons keep sequence length at 1,536 tokens.The predicted-plan continuation uses a 70/30 reference/predicted-plan mixture.Source: Appendix G.3 · p. 54

Appendix G.4. Decoding, checkpoint selection, and repair

  • Generation is normally greedy and single-shot, with one fixed string-level repair pass and no execution-error feedback or regeneration.The controlled direct-latent run restores its best validation checkpoint, whereas the plan-mediated run is evaluated at its final step.Source: Appendix G.4 · pp. 54–55

Appendix G.5. Single-run scope

  • Each trained condition is a single run, so comparisons estimate sample variation conditional on checkpoints rather than seed-to-seed variation.A multi-seed replication of the B1a–B2-Pred coverage comparison was not completed, and the manuscript makes no claim about its stability across seeds.Source: Appendix G.5 · p. 55

Appendix G.6. Implementation-specific limitations

Table G.1 collects implementation-specific limitations and the changes required to address them. These are distinguished from methodological limitations because they can, in principle, be changed without altering the construction-mediated formulation.

Appendix G.6. Implementation-specific limitations

  • The paper separates these implementation-specific issues from methodological limitations because they can, in principle, be changed without changing the overall formulation.The referenced table collects the implementation details and their corresponding changes.Source: Appendix G.6 · p. 55, Table G.1 · p. 56
  • Table G.1 is devoted to implementation-specific limitations and changes proposed to address them.Its scope is implementation details rather than methodological limitations.Source: Appendix G.6 · p. 55, Table G.1 · p. 56
  • The table's stated purpose is to connect implementation-specific limitations with the changes required to address them.The paper treats these changes as separable from the construction-mediated method itself.Source: Appendix G.6 · p. 55, Table G.1 · p. 56

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