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GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedback
Giorgio Giannone, Anna Clare Doris, Amin Heyrani Nobari, Kai Xu, Akash Srivastava, Faez Ahmed
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Summary
GIFT (Geometric Inference Feedback Tuning) is a data augmentation framework for Image-to-CAD program synthesis that leverages geometric feedback to improve model robustness and performance. It uses two mechanisms: Soft-Rejection Sampling (GIFT-REJECT) to incorporate diverse high-fidelity programs, and Failure-Driven Augmentation (GIFT-FAIL) to train on near-miss predictions. By amortizing inference-time search into model parameters, GIFT reduces inference compute by 80% and improves mean IoU by 12% over supervised baselines.
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GIFT → includes → GIFT-REJECT
confidence 100% · GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT)
GIFT → includes → GIFT-FAIL
confidence 100% · and Failure-Driven Augmentation (GIFT-FAIL)
GIFT → uses → OpenCASCADE
confidence 95% · we compute a geometric validity function f(z) using a CAD kernel (e.g., OpenCASCADE)
GIFT → improves → GenCAD-Code
confidence 90% · GIFT... uses offline geometric feedback to convert inference-time samples into augmented supervised training data.
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Abstract
Abstract:Generating executable CAD programs from images requires alignment between visual geometry and symbolic program representations, a capability that current methods fail to learn reliably as design complexity increases. Existing fine-tuning approaches rely on either limited supervised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the primary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training examples that align visual geometry with program syntax. This limitation is especially acute because the collection of diverse and verified engineering datasets is both expensive and difficult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages geometric feedback to turn test-time compute into a bootstrapped set of high-quality training samples. GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT), which retains diverse high-fidelity programs beyond exact ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which converts near-miss predictions into synthetic training examples that improve robustness on challenging geometries. By amortizing inference-time search into the model parameters, GIFT captures the benefits of test-time scaling while reducing inference compute by 80%. It improves mean IoU by 12% over a strong supervised baseline and remains competitive with more complex multimodal systems, without requiring additional human annotation or specialized architectures.
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- Source: https://arxiv.org/abs/2603.27448v1
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GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedback Giorgio Giannone 1 2 Anna Clare Doris 2 Amin Heyrani Nobari 2 Kai Xu 1 Akash Srivastava 3 4 Faez Ahmed 2 Abstract Generating executable CAD programs from im- ages requires alignment between visual geometry and symbolic program representations, a capa- bility that current methods fail to learn reliably as design complexity increases. Existing fine- tuning approaches rely on either limited super- vised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the pri- mary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training ex- amples that align visual geometry with program syntax. This limitation is especially acute be- cause the collection of diverse and verified en- gineering datasets is both expensive and diffi- cult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages ge- ometric feedback to turn test-time compute into a bootstrapped set of high-quality training sam- ples. GIFT combines two mechanisms: Soft- Rejection Sampling (GIFT-REJECT), which re- tains diverse high-fidelity programs beyond ex- act ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which converts near- miss predictions into synthetic training examples that improve robustness on challenging geome- tries. By amortizing inference-time search into the model parameters, GIFT captures the benefits of test-time scaling while reducing inference com- pute by 80%. It improves mean IoU by 12% over a strong supervised baseline and remains com- petitive with more complex multimodal systems, without requiring additional human annotation or specialized architectures. 1 AI Innovation Team, Red Hat 2 DeCoDE Lab, MIT 3 Core AI, IBM 4 MIT-IBM Watson AI Lab.Correspondence to: <ggiorgio@mit.edu>. Preprint. 1. Introduction From its theoretical origins (Ross &Rodriguez, 1963; Coons, 1963; Mäntylä, 1987), Computer-Aided Design (CAD) has evolved into the cornerstone of modern engineering, enabled by the sophisticated modeling capabilities of geometric ker- nels (Piegl &Tiller, 2012). 12345678910 K 0.70 0.72 0.74 0.76 0.78 0.80 0.82 IoU GIFT GIFT-REJECT SFT Figure 1. Efficiency vs. Performance. We compare Pass@k (test set IoU) across compute budgets. GIFT (green) matches the peak performance of the CAD-Coder-SFT baseline (orange) while using 80% less compute (requiring far fewer samples). GIFT outper- forms both SFT and GIFT-REJECT at every compute level, demon- strating that self-training with geometric feedback significantly enhances image-conditional CAD generation. Results reflect mean IoU on the GenCAD test subset, including failure cases. An ex- tended scaling analysis is provided in Appendix C (Figure 12). Deep generative modeling is transforming engineering de- sign, offering new solutions to complex, high-dimensional problems (Ahmed et al., 2025; Regenwetter et al., 2022; Song et al., 2023). Recent empirical successes highlight the versatility of these methods in tasks such as topology opti- mization (Nie et al., 2021; Mazé &Ahmed, 2023; Giannone et al., 2023; Nobari et al., 2025), mechanism linkage de- sign (Nobari et al., 2024), vehicle dynamics (Elrefaie et al., 2024), and CAD generation (Alam &Ahmed, 2024). While researchers have developed direct forward models to synthesize 3D shapes from diverse inputs like point clouds, images, and text (Alam &Ahmed, 2024; Yu et al., 2025; Tsuji et al., 2025), these approaches face a critical bottle- neck: the output format. Existing generative models (Lam- bourne et al., 2021; Li et al., 2025b) typically yield tessel- 1 arXiv:2603.27448v1 [cs.LG] 28 Mar 2026 Geometric Inference Feedback Tuning Method IoU Median Mean 0.846 0.695 0.905 0.742 0.948 0.781 SFT GIFT-REJECT GIFT (a) Accuracy. SFTGIFT-REJECTGIFT 200 300 400 500 600 700 800 900 1000 Number of Tokens (Ground Truth) (b) Complexity - Tokens. Task Complexity 0.5 0.6 0.7 0.8 0.9 IOU SFT GIFT-REJECT GIFT (c) Performance vs Task Com- plexity. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Problems Solved SFT GIFT-REJECT GIFT +31.4% +53.8% (d) Ratio Problems Solved. Figure 2. Robustness Analysis. (a) GIFT achieves superior accuracy (Mean/Median IoU). (b,c) While all models degrade with increased task complexity (token length), GIFT maintains higher resilience than SFT. (d) GIFT solves 53% more problems compared to the baseline, highlighting the benefit of diverse training data. lated meshes (STL) or Boundary Representations (B-Rep, STEP). These formats are inherently verbose and topologi- cally complex, making them difficult for engineers to param- eterize or edit. Moreover, the need for specialized 3D de- coders or large language models to generate such structures imposes significant computational and structural overhead. Modality-to-Program To circumvent these limitations, a growing paradigm leverages high-level symbolic pro- grams (Bhuyan et al., 2024; Hewitt et al., 2020; Jones et al., 2022) as an intermediate representation. Unlike rigid geo- metric formats, code offers a compact and editable struc- ture (Ganeshan et al., 2023) that is naturally amenable to autoregressive language modeling - a property that has al- ready proven effective in domains such as mathematical reasoning (Guo et al., 2025) and visual-language ground- ing (Surís et al., 2023). This approach effectively abstracts geometry into parametric operations, though it necessitates an execution environment (e.g., a geometric kernel like OpenCASCADE 1 ) to render the generated code into valid CAD formats. Despite this dependency, the modality-to- program strategy has gained significant traction in recent literature (Doris et al., 2025; Kolodiazhnyi et al., 2025; Li et al., 2025c; Rukhovich et al., 2025; Wang et al., 2025b), with a particular emphasis onCadQuery 2 , a Python-based scripting language for parametric CAD design. Post-Training The dominant paradigms for post- training (Ouyang et al., 2022) are Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL). SFT provides a foundation for CAD generation but often suffers from weak alignment between visual features and program syntax. Recent works attempt to mitigate this by con- ditioning on auxiliary modalities such as point clouds and depth maps, though reliance on ad-hoc architectures limits model generality (Wang et al., 2025b; Chen et al., 1 https://github.com/Open-Cascade-SAS/OCCT 2 https://github.com/CadQuery/cadquery 2025). RL can improve alignment and performance but is resource-intensive (Schulman et al., 2017; Guo et al., 2025), incurring high memory and communication costs due to the need to execute CPU-bound CAD kernels during online training (Li et al., 2025c; Kolodiazhnyi et al., 2025). We argue, however, that the primary bottleneck in SFT and RL post-training for engineering design is not model qual- ity or algorithmic sophistication, but the fine-tuning data itself. Our approach is motivated by a simple observation: advances in LLMs and VLMs have been driven largely by high-quality, diverse datasets, yet assembling such data for data-driven engineering design remains expensive. Data augmentation offers a natural remedy, but the central chal- lenge is determining how to use available compute most effectively to address model strengths and weaknesses while exploiting the structural properties of the underlying engi- neering problem. To address these limitations, we introduce Geometric Infer- ence Feedback Tuning (GIFT), a framework for verifier- guided data augmentation in Image-to-CAD generation. GIFT uses offline geometric verification to mine diverse valid programs and structured near-miss failures, convert- ing them into a high-quality augmented training set. By distilling the benefits of test-time search into the training data, our approach improves generation quality while reduc- ing inference cost and avoiding the complexity of online reinforcement learning. GIFT separates exploration from learning: candidate pro- grams are generated and verified offline during inference- time sampling, then used for standard supervised updates. This design preserves the benefits of reinforced geomet- ric feedback without introducing the instability of online training. Contributions Our key contributions are: • We introduce Geometric Inference Feedback Tuning 2 Geometric Inference Feedback Tuning (GIFT), a scalable data augmentation framework for Image-to-CAD program synthesis that uses offline geo- metric feedback to convert inference-time samples into augmented supervised training data. •We propose a dual augmentation strategy: Soft- Rejection Sampling (GIFT-REJECT), which adds di- verse geometrically valid alternative programs as new output targets, and Failure-Driven Augmentation (GIFT-FAIL), which renders near-miss predictions into synthetic inputs paired with the original ground-truth code. • We show that this augmentation pipeline expands the effective training set substantially, improves single- shot accuracy over a strong supervised baseline, and reduces the reliance on expensive test-time sampling. •We demonstrate through extensive analysis that GIFT improves robustness on complex geometries, narrows the amortization gap between pass@1 and pass@k, and remains competitive with more complex multimodal systems without requiring additional human annotation or specialized architectures. 2. Background Vision-Language Models Vision-Language Models (VLMs (Liu et al., 2024; Bai et al., 2025)) are powerful foundation models that integrate Large Language Models (LLMs) with vision encoders to process visual information (Fig. 4). These systems are highly versatile, supporting diverse tasks such as visual captioning, QA, multitasking, referring expressions, and code generation.Although aligning visual and textual components remains an open challenge, recent VLMs based on Qwen have established strong baselines. Base Prompt Image VLMCode STEP FILE Generation Geometric Alignment STEP FILE GT IoU Figure 3. The CAD-Coder pipeline processes multimodal inputs (text prompts and images) to generate executable CAD code. This code is converted into STEP files via geometric alignment and validated against the ground truth using IoU metrics. Image-Conditional CAD Program SynthesisImage-to- CAD (Alam &Ahmed, 2024; Li et al., 2025c; You et al., 2025) remains a central challenge in generative design. Re- cently, CAD-Coder (Doris et al., 2025) introduced an end- to-end pipeline to bridge the gap between 2D images and parametric code (Fig. 3). Its three-stage workflow utilizes a visual encoder (e.g., LLaVA (Liu et al., 2024) or Qwen- VL (Bai et al., 2025)) to project geometric features into language embeddings, employs an autoregressive LLM to generate executable CadQuery scripts, and executes the code via a Python interpreter to reconstruct B-Rep models. The system is trained via Supervised Fine-Tuning (SFT) on the 160k image-code pairs of the GenCAD-Code dataset (Alam &Ahmed, 2024; Doris et al., 2025). The training optimizes a standard next-token prediction objective: F SFT (θ) =E (x,c)∼D SFT [logp θ (x|c)] = X c T X t=1 logp θ (x t | x <t , c), (1) which aligns visual semantics with strictCadQuerysyntax using a standard MLE estimator. Here,crepresents the input image and a fixed text prompt ("generate cadquery code for the image"). Andxrepresents the model output, i.e. code or a CAD format. We adopt this baseline algorithm to train our GIFT models across varying data sources. Limitations Current methods face significant hurdles. First, SFT is brittle: it enforces a rigid one-to-one map- ping that penalizes valid alternative programs yielding the same geometry, while also relying on scarce, low-diversity datasets. Second, RL is complex and fragile; it requires intricate training pipelines and specialized infrastructure, making reproduction difficult. Finally, scaling is computa- tionally inefficient due to hardware bottlenecks; specifically, reward calculation relies on CPU-based CAD solvers, the constant communication overhead with GPU-based models severely limits performance scaling. See Appendix A for additional discussion. 3. Method We argue that the main bottleneck in image-conditional CAD generation is not model capacity, but modality align- ment: the scarcity of diverse supervised examples that con- nect visual geometry to valid program structure. To address this limitation, we introduce GIFT, a verifier-guided data augmentation framework. Rather than relying solely on the original image-code pairs, GIFT samples candidate pro- grams from a pretrained image-to-CAD model, evaluates them with a geometric kernel, and converts geometrically valid and near-valid generations into additional supervised training examples. Operationally, GIFT transforms inference-time search into an offline augmentation pipeline (Algorithm 1). For each training image, high-quality alternative programs are re- tained as additional targets for the original input, while structured near-miss failures are rendered back into the im- age domain and paired with the ground-truth code. The resulting augmented dataset improves both output diver- 3 Geometric Inference Feedback Tuning sity and robustness without requiring online reinforcement learning or additional human annotation. Program Synthesis as Latent Reasoning While multi- ple distinct programs can generate the same correct output, most engineering datasets provide only a one-to-one map- ping. Consequently, it is challenging to steer the genera- tive process to encourage diversity while simultaneously respecting the underlying data distribution. This creates an unnecessarily narrow training signal. We model Image-to-CAD generation as a conditional latent- program problem, where the goal is to learn a distribution over programszthat can decode to the correct geometryx rather than a single canonical string: p θ (x, z|c) = p(x|z, c) p θ (z|c),(2) wherexdenotes the decoded CAD representation (B-rep, mesh),zrepresents the latent program (incadquerysyn- tax), andcis the conditioning input, consisting of a single image and a short, fixed textual prompt. For CAD recon- struction, the conditional distributionp(x|z, c)can be ap- proximated as a deterministic decoding stepx = d(z, c). This decoding is typically non-learned, relying on standard CAD tools to convert code into formats such as STEP files. Therefore, image-conditional program synthesis focuses on learning an expressive p θ (z|c), typically via SFT and RL. Inference-Time Scaling for CAD Generation We use Inference-Time Scaling (ITS (Brown et al., 2024; Snell et al., 2024)) primarily as a data-generation tool rather than as a deployment strategy. For each training image, we sample multiple candidate programs from the base model and verify them against the ground-truth geometry using a CAD kernel. The verified samples are then partitioned into three groups: exact or near-exact solutions, recoverable near-miss failures, and unrecoverable failures. This post-hoc analysis enables us to construct an augmented training set that both broadens the target distribution and explicitly trains on hard cases. This procedure provides a form of weak supervision. Instead of treating only exact string matches as correct, we retain any program that produces sufficiently accurate geometry. In doing so, we shift training toward better coverage of the valid solution space rather than a single canonical program: z (k) K k=1 ∼ p θ (z|c).(3) Crucially, because this feedback requires a CAD kernel and ground-truth programs for verification, we restrict aug- mentation to the original training distribution and do not introduce any additional human-crafted supervision. Bootstrapping We generate candidate programs using QwenVL-2.5-7B-CadCoder(Doris et al., 2025), utiliz- ing ground truth STEP files in the GenCad-Code trainset for geometric feedback. To ensure sampling diversity, we employ a scaling strategy across five computational budgets (N ∈ 8, 16, 32, 64, 128). We apply an inverse hyper- parameter strategy: lower budgets use wider temperature ranges to maximize exploration, while higher budgets en- force strict low-temperature sampling to prioritize precision. Full sampling configurations are detailed in Table 10, Ap- pendix F and I. 3.1. Geometric Inference Feedback Tuning LetD SFT = (c (n) , z (n) gt ) N n=1 be a training dataset ofN image-program pairs, wherecis the visual input andz gt is the ground truth CAD program (Fig. 5). We denote the base policy (the base Image-to-Code model (Doris et al., 2025)) as p θ (z|c). For each inputc, we perform inference-time scaling by sam- pling a set ofKcandidate programsZ K from the current policy: Z K =z (k) K k=1 ∼ p θ (z|c). For every candidatez ∈ Z K , we compute a geometric validity functionf (z)using a CAD kernel (e.g., OpenCAS- CADE) to measure alignment with the ground truth: f (z) = IoU(Execute(d(z))), Execute(d(z gt ))), whered(z)projects code to a format amenable to the CAD kernel (STEP or STL files), andExecuteruns the geometric kernel to obtain the final 3D model as a B-Rep or Mesh representation, and the Intersection-over-Union (IoU) is computed between the generated and ground truth CAD models. In the following we will use the shorthandf (z) := IoU(z, z gt ) for simplicity. We employ two complementary augmentation mechanisms: Soft Rejection Sampling (SRS) and Failure-Driven Aug- mentation (FDA). SRS augments the output space (code) by capturing diverse valid programs to limit memorization, while FDA augments the input space (image) to specifically target hard failures. Through repeated sampling, this approach constructs an aug- mented training set whose composition reflects the model’s inference behavior across compute budgets. Threshold Selection We choose the filtering thresholds empirically from the cumulative distribution of inference- time IoU scores (Fig. 9 and 8). We setτ low = 0.5because roughly 10% of generated programs fall below this level; these samples are typically degenerate or non-executable and are excluded from the training pool. We setτ valid = 0.9 to separate high-quality solutions from recoverable failures. Approximately 40% of samples fall below this threshold. This yields a natural dual strategy: Soft-Rejection Sampling 4 Geometric Inference Feedback Tuning Generate a description for this image Image-to-Text (a) Image-to-Text (Generalist VLM). Generate cadquery code for this image Image-to-CAD (b) Image-to-CAD (Specialist VLM). Figure 4. Comparison of Vision-Language Model generations: (a) standard text description vs. (b) executable CAD code. Image-to- Code SFT Figure 5. Standard SFT Baseline. The model is trained on static image-code pairs using a next-token prediction objective. uses the high-fidelity tail (IoU≥ 0.9), while Failure-Driven Augmentation targets near-miss failures (0.5≤ IoU < 0.9). Soft Rejection Sampling: Output Augmentation Stan- dard rejection sampling typically selects only the single best sample or strictly correct programs (f (z) = 1). This lim- its diversity. To overcome this, SRS utilizes the feedback from the setZ K to identify a broader set of valid programs (Fig. 6). We define a selection indicatorw srs (z)that filters Image-to- Code 0.93 0.95 0.71 SRS Figure 6. Soft Rejection Sampling (SRS). We sampleKprograms, verify them with a geometric kernel, and retain diverse valid pro- grams (0.9≤ IoU < 0.99) to expand the training distribution beyond the single ground truth. for high-fidelity alternatives that are distinct from the exact ground truth: w srs (z) = 1 [τ valid ≤ f (z) < τ match ], whereτ valid = 0.9andτ match = 0.99. The resulting SRS datasetD SRS expands the training targets by including these diverse valid solutions: D SRS = [ (c,z)∈D (c, z)| z∈Z K , w srs (z) = 1. This procedure broadens the training distribution by includ- ing multiple high-quality programs for the same input. As a result, the model is less likely to collapse onto a single rigid syntactic pattern. This trades exact string matching for greater diversity and coverage in program space. The thresholdτ valid preserves geometric quality while still allowing meaningful variation in program form. We follow the analysis in Fig. 9b to choose the thresholds for τ . Exploiting Geometric FeedbackAlthough soft labeling and output augmentation are well established in self-training and weak-supervision settings (Dong et al., 2023; Zelikman et al., 2024), GIFT differs in how it obtains the signal. In- stead of relying on heuristic confidence scores or learned rewards, it uses a deterministic geometric kernel to identify novel, valid alternative programs. This makes it possible to expand the target distribution with high-quality synthetic supervision drawn directly from the original training set. Image-to- Code 0.54 0.38 0.71 FDA Figure 7. Failure-Driven Augmentation (FDA). We identify hard negatives (programs with0.5≤ IoU < 0.9), render them into synthetic images (φ(z)), and train the model to map these ’noisy’ inputs back to the correct ground truth code (z gt ). 5 Geometric Inference Feedback Tuning Learning from Failure: Input Augmentation While SRS reinforces successful and diverse outputs, it does not directly address persistent failure cases. To do so, we use programs that are geometrically plausible yet remain incor- rect across both small and large sampling budgets inZ K . These near-miss samples provide a useful signal because they encode structured errors rather than random noise. We define a failure indicatorw fda (z)to select these hard nega- tives: w fda (z) = 1 [τ low ≤ f (z) < τ valid ], whereτ low = 0.5(see analysis in Fig. 9b). Unlike SRS, which pairs the sampled code with the original image, FDA uses the sampled code to construct a challenging input (Fig. 7). We define a rendering functionφthat projects the CAD model back into the input image domain, i.e. ̃ c← φ(d(z)). Sincezis a valid executable program, we can render it into a synthetic image ̃ c . This synthetic image represents the visual manifestation of the model’s geometric error. The FDA datasetD FDA consists of pairs mapping the failed visual state back to the original ground truth: D FDA = [ ( ̃ c,z gt )∈D (φ(d(z)), z gt )| z∈Z K , w fda (z) = 1. This turns FDA into a geometric denoising objective: the model receives an imperfect rendered input ̃ cand is trained to recover the corresponding ground-truth programz gt . In practice, this improves robustness to visual ambiguity and partial geometric mismatch. Objective The final GIFT objective amortizes the expen- sive inference-time search into the model weights by op- timizing the log-likelihood over the combined augmented datasets: F GIFT (θ) =E (c,z)∼D SFT [logp θ (z|c)] | z Base (SFT) + E (c,z)∼D SRS [logp θ (z|c)] | z Output Diversity (SRS) +E (c,z)∼D FDA [logp θ (z|c)] | z Input Robustness (FDA) . (4) Note thatw srs andw fda operate on disjoint intervals of IoU (valid vs. near-miss), ensuring distinct gradient signals. In practice, sampling imagesc (n) and programsz (n) gt from the training setD SFT , and generatingKMonte Carlo samples from the base model for eachc (n) ,z (k) K k=1 ∼ p θ (z|c (n) ), we obtain the empirical objective: ̃ F GIFT (θ)∝ N X n=1 logp θ (z (n) gt |c (n) ) + N X n=1 K X k=1 w srs (z (k) ) logp θ (z (k) |c (n) ) + N X n=1 K X k=1 w fda (z (k) ) logp θ (z (n) gt | ̃ c (k) ), (5) where we omit the indexnoverz (k) for clarity. ̃c (k) here is the output of the inverse mappingφ(d(z (k) ))andz (k) ∼ p θ (z|c (n) )is a sample from the model conditioning on an image. The final training loss is minimized asL(θ) = − ̃ F GIFT (θ)/N . We provide a detailed gradient analysis of this objective in Appendix G. 4. Experiments DatasetWe conduct our evaluation on the GenCAD-Code dataset (Alam &Ahmed, 2024), derived from the DeepCAD dataset (Wu et al., 2021), which contains 163k image-code pairs of parametric CAD designs for train, and 8k image- code pairs for testing. We additionally evaluate on a cu- rated set of 400 out-of-distribution (OOD) samples (Doris et al., 2025) that present realistic input images not well- represented in the training distribution. Baselines We use three primary vision-language models: Qwen-VL-2.5-7B-Instruct and Qwen-VL-2.5-3B-Instruct as base multimodal foundation models, and CAD-Coder- SFT (7B) as the main supervised fine-tuning baseline and sampling model. The CAD-Coder-SFT model serves as our starting point for exploring geometric inference feedback tuning. In the following we refer to CAD-Coder-SFT as SFT. Setup We evaluate three training configurations: (i) stan- dard Supervised Fine-Tuning (SFT) as our baseline, (i) GIFT with Soft-Rejection Sampling (SRS), which captures diverse valid programs beyond ground-truth matching, and (i) GIFT with both SRS and Failure-Driven Augmenta- tion (FDA), which additionally targets hard examples where the base model consistently struggles. Through our SRS and FDA strategies, we expand the original 163k training set to approximately 370k samples (Appendix F and I). We train all models for a maximum of 10 epochs or when performance stops improving for two consecutive epochs. Empirically, models converged within 3 to 4 epochs. In the following, we use GIFT-REJECT to denote the model trained with SRS, GIFT-FAIL for the one trained with FDA, and GIFT to denote the model trained with both SRS and FDA. 6 Geometric Inference Feedback Tuning Evaluation and Geometric VerifierWe use IoU as main metric as proposed in (Doris et al., 2025). GIFT relies heavily on geometric kernels (OpenCASCADE) for IoU computation. For the specific calculation, we follow the IoU-best protocol from (Doris et al., 2025; Li et al., 2025c). In particular, we first execute the generated CadQuery script to obtain a Boundary Representation (B-Rep) solid. We then normalize both the generated and ground-truth solids by centering and scaling them based on the trace of their inertia tensor. To address the ambiguity in orientation, we align their principal axes and compute the Intersection-over- Union (IoU) across different axis permutations, defining IoU-best as the maximum value obtained. This ensures the verification is robust to rigid transformations and coordinate system mismatches. 4.1. Inference-Time Scaling: Analysis We first investigate the latent capabilities of the base CAD- Coder model by analyzing its scaling behavior on the train- ing set. We employ Inference-Time Scaling (ITS) with varying computational budgetsN ∈ 8, 16, 32, 64, 128, generating multiple program candidates per image and fil- tering them via geometric verification (IoU against ground truth). Table 1. Performance comparison between Top-10% and Top-1 inference-time selections on the GenCAD training subset. We report the mean IoU obtained by retaining either the top 10% of generated samples or only the single best sample per input, with and without exact ground-truth matches. ExpConditionBudget NInputOutput Mean (Image)(Code) IoU Top 10% w/ IoU=1(8, 16, 32, 64, 128)4k169,116 0.734 w/o IoU=1 (8, 16, 32, 64, 128)4k134,345 0.665 IoU Best (Top1) w/ IoU=1(8, 16, 32, 64, 128)4k3,911 0.839 w/o IoU=1 (8, 16, 32, 64, 128)4k2,619 0.760 Performance Gap As shown in Table 1, there is a sig- nificant disparity between the model’s average and peak performance. While the mean IoU for the top 10% of sam- ples is 0.734, selecting the single best sample (Top-1) boosts performance to 0.839. This gap indicates that the model fre- quently generates valid solutions that are discarded during standard greedy decoding, confirming that significant learn- ing signal remains unexploited within the model’s weights. Failure Modes Figure 8 visualizes the IoU distribution of generated samples. Even when filtering for the best can- didates (Fig. 8c), the distribution remains bimodal: a large cluster of high-fidelity solutions contrasts with a persistent tail of failures where the model cannot recover correct ge- ometry regardless of sampling budget. Notably, removing exact ground-truth matches (Fig. 8d) reveals a rich set of alternative valid programs (0.9 < IoU < 0.99), which we 0.00.20.40.60.81.0 IoU 10 3 10 4 Frequency (a) All samples 0.00.20.40.60.81.0 IoU 10 3 Frequency (b) All samples w/o GT 0.00.20.40.60.81.0 IoU 10 1 10 2 10 3 Frequency (c) Best samples 0.00.20.40.60.81.0 IoU 10 1 10 2 Frequency (d) Best samples w/o GT Figure 8. IoU distributions for samples obtained via ITS, selecting the top 10% and top-1 programs per image. Panels show: (a) all samples; (b) all samples excluding ground truth (GT) matches; (c) best-performing samples; and (d) best samples excluding GT. The persistence of low-quality generations, even in the best-performing subset, highlights the need to amortize offline ITS feedback to improve base model reliability. can leverage to improve data coverage. 2 3 2 4 2 5 2 6 2 7 Budget (N) 0.70 0.75 0.80 0.85 0.90 IoU (Pass@N) Best IoU Mean IoU Median IoU (a) Best IoU Scaling. 0.10.20.30.40.50.60.70.80.91.0 IoU Threshold ( ) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fraction Samples with IoU < (b) IoU Threshold. Figure 9. Analysis of inference-time IoU statistics. (a) Pass@N scaling shows that best-case performance improves with compute budget, while mean and median gains saturate more quickly. (b) The cumulative IoU distribution motivates the filtering thresholds used for SRS and FDA by separating low-quality failures from high-fidelity solutions Scaling Limits Figure 9 demonstrates that while perfor- mance improves with budgetN, returns diminish rapidly. Simple stochastic sampling often introduces syntactic errors rather than semantic diversity. This suggests that merely scaling inference is inefficient; instead, we must amortize these expensive successful search paths back into the model. 4.2. Amortizing Inference-Time Augmentation The significant performance disparity between Top-1 and Top-10% generations drives our inference-time compute- driven data augmentation strategy. To tune the model, we leverage high-fidelity candidates via Soft-Rejection Sam- 7 Geometric Inference Feedback Tuning SFT (mean) GIFT-REJECT (mean) GIFT (mean) SFT (median) GIFT-REJECT (median) GIFT (median) 0.65 0.70 0.75 0.80 0.85 0.90 0.95 IoU +6.8% +12.4% +7.0% +12.1% Figure 10. GIFT strategies impact. We compare the SFT baseline against GIFT-REJECT (targeting output diversity) and the full GIFT framework (combining diversity and robustness). The full GIFT method yields the largest performance gain, confirming the critical value of learning from hard negatives. pling to expand solution coverage, while utilizing Failure- Driven Augmentation to specifically target inputs where the model consistently fails. Efficiency We further analyze the computational effi- ciency of our method by comparing the inference-time scal- ing curves (Figure 1). The GIFT model consistently outper- forms the SFT baseline at every level of compute budget (Table 2). GIFT matches the peak performance of the SFT model (achieved via extensive rejection sampling) while re- ducing the inference compute requirement by approximately 80% (Figure 1). This confirms that GIFT successfully dis- tills the benefits of test-time search directly into the model weights. An extended version of this scaling analysis, in- cluding the GIFT-FAIL variant, is provided in Appendix C (Figure 12), where the same ordering holds across inference budgets. SFT GIFT-REJECT GIFT 0.66 0.68 0.70 0.72 0.74 BLEU Score +3.7% +8.7% (a) BLEU. SFT GIFT-REJECT GIFT 0.76 0.78 0.80 0.82 0.84 METEOR Score +1.4% +4.9% (b) METEOR. SFT GIFT-REJECT GIFT 0.80 0.82 0.84 0.86 0.88 ROUGE Score +0.2% +2.2% (c) ROUGE. Figure 11. Evaluation results on standard captioning metrics for SFT and GIFT variants. Performance We evaluate the impact of these strategies on the test set, as shown in Figure 10. The baseline SFT model achieves a mean IoU of 0.698. The GIFT-REJECT strategy significantly boosts this performance by exposing the model to a diverse set of valid programs. Adding Failure- Driven Augmentation (full GIFT augmentation framework) further improves generalization, increasing mean IoU from 0.698 to 0.782. We also observe consistent gains on standard text-generation metrics, including BLEU, METEOR, and ROUGE (Fig- ure 11). These improvements suggest that GIFT better aligns generated program syntax with the distribution of valid target code. Amortization Gap We quantify the amortization gap as the difference between single-shot performance (pass@1) and oracle performance under repeated sampling (pass@k). As shown in Table 3, the SFT baseline has a gap of 15.5%, indicating substantial reliance on rejection sampling to achieve high performance. GIFT-REJECT reduces this gap to 10.9%, while the full GIFT model reduces it further to 5.2%, a 66.4% relative reduction compared with the base- line. These results show that GIFT shifts probability mass toward high-quality outputs, improving performance even without extensive test-time sampling. 4.3. Intrinsic Metrics To further analyze the robustness of our approach, we exam- ine the relationship between model performance and task complexity, where complexity is proxied by the token length of the ground truth CAD programs (Fig. 2b). As illustrated in Fig. 2c, while all models exhibit an expected degradation in performance as the geometric complexity increases, the models trained with GIFT demonstrate significantly greater resilience compared to the SFT baseline. The performance gap becomes particularly pronounced at higher complexity levels, where the baseline SFT model’s accuracy drops sharply. In contrast, GIFT maintains a more stable performance profile, effectively mitigating the curse of complexity often observed in autoregressive code generation. This suggests that by incorporating hard neg- atives through Failure-Driven Augmentation (FDA) and diverse valid solutions via Soft-Rejection Sampling (SRS), the model learns to sustain geometric coherence even for intricate designs requiring longer program sequences. Ap- pendix D expands this analysis with finer-grained complex- ity breakdowns and distributional statistics over operations and token lengths (Figure 16 and 17). 4.4. General Evaluation Table 4 compares GIFT with recent modality-to-CAD sys- tems across several input settings, including depth, point 8 Geometric Inference Feedback Tuning Table 2. Test-set IoU across increasing inference-time compute budgets for CAD-Coder-SFT, GIFT-REJECT, GIFT-FAIL, and the full GIFT model. The final row reports the relative improvement of GIFT over the SFT baseline at each budget. Method12345678910 SFT0.6980.7250.7430.7630.7800.7880.7920.8010.8040.807 GIFT-REJECT0.7320.7450.7620.7730.7850.7960.8020.8070.8100.812 GIFT-FAIL0.7610.7800.7890.7910.7990.8020.8020.8030.8030.806 GIFT0.7790.8020.8090.8110.8120.8160.8160.8170.8180.819 ∆(GIFT,SFT ) +11.60 % +10.53 % +8.92 % +6.31 % +4.04 % +3.52 % +3.02 % +2.01 % +1.80 % +1.56 % Table 3. Mean IoU on the GenCAD test set and amortization gap between pass@1 and pass@k under different dataset-augmentation strategies. Smaller gaps indicate that model quality is better amor- tized into single-shot generation. Methodpass@1 pass@5 pass@10Gap∆ SFT0.6980.7760.80715.5 %- GIFT-REJECT0.7320.7880.81210.9 % -29.6 % GIFT-FAIL0.7610.7920.8065.9 %-61.9 % GIFT0.7770.8120.8205.2 %-66.4 % clouds, text, multi-view images, and single-view images. Despite using only a single-view image as input, GIFT deliv- ers competitive performance relative to methods that rely on richer modalities such as point clouds or multi-view supervi- sion. In Table 8 we provide evidence of sensitivity to failed rendering (code that cannot be compiled) for modality-to- code models, and show how median values are more reliable and stable than mean values for such problems. Table 4. Comparison with recent modality-to-CAD systems trained on DeepCAD variant datasets under single-sample inference. In- puts include point clouds (PC), text (TXT), multi-view images (IMG), and single-view images (IMG-s). ModalityIoU frontier zero-shot GPT4oIMG-s0.378 Gemini-2.5-PROIMG-s0.451 Gemini-3.0-PROIMG-s0.540 open-source zero-shot Qwen-2.5-72B (Bai et al., 2025)IMG-s0.345 open-source finetuned PointNet (Wu et al., 2021)PC0.467 PointBERT (Xu et al., 2023)PC0.653 TransCAD (Dupont et al., 2024)PC0.655 PrismCAD (Lambourne et al., 2022)PC0.721 Point2Cyl (Uy et al., 2022)PC0.738 CAD-Diffuser (Ma et al., 2024)PC0.743 CAD-SigNet (Khan et al., 2024a)PC0.773 Text2CAD (Khan et al., 2024b)TXT0.715 Cadrille (Kolodiazhnyi et al., 2025)PC0.794 Cadrille-RL (Kolodiazhnyi et al., 2025) PC,IMG,TXT0.859 GACO-CAD-RL (Wang et al., 2025b)IMG-s,Depth,Normal 0.864 ReCAD-VL (Li et al., 2025c)IMG-s0.631 CAD-Coder-SFT (Doris et al., 2025)IMG-s0.691 CAD-Coder-GIFT (ours)IMG-s0.782 Table 5. Ablation of GIFT variants on the GenCAD test set. AUG denotes standard augmentation. MethodIoU SFT (LONG)0.698 SFT w/ AUG0.710 GIFT-REJECT0.742 GIFT-REJECT w/ AUG 0.745 GIFT-FAIL0.761 GIFT0.782 Ablations Table 5 iso- lates the contribution of each component of GIFT. Naive augmentation pro- vides only marginal gains, whereas GIFT-REJECT im- proves performance by min- ing diverse valid programs and GIFT-FAIL improves ro- bustness by targeting recov- erable errors in the 0.5-0.9 IoU range. Combining both mechanisms yields the strongest overall performance, confirming that diversity and failure correction contribute complementary benefits. Extended ablations in Appendix C confirm these benefits persist across diverse model architectures (Fig. 13) and sam- pling temperatures (Fig. 14), with strong generalization to out-of-distribution geometries. Finally, in Fig. 15 we run preliminary experiments to eval- uate out-of-distribution performance and assess general- ization beyond the in-distribution setting using real world images as input. Table 7 provides valid samples rates and error analysis for in- and out-of-distribution test splits. 5. Limitations and Conclusion We presented Geometric Inference Feedback Tuning (GIFT), a verifier-guided data augmentation framework for Image- to-CAD program synthesis. By using a CAD kernel to mine both diverse valid outputs and structured failure cases, GIFT converts inference-time search into additional supervised training signal. Empirically, this produces stronger single- shot generation, reduces dependence on inference compute, and narrows the gap to more complex multimodal systems. Limitations Our approach relies on a deterministic ge- ometric kernel and ground-truth CAD programs to verify generated samples, which currently limits its application in purely unsupervised or "in-the-wild" settings where such verifiers are unavailable. 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Related Work Generative Models for CAD Generative design is experiencing a widespread resurgence across engineering domains, from topology optimization to mechanism synthesis (Regenwetter et al., 2022; Mazé &Ahmed, 2023; Nobari et al., 2024). Early approaches to CAD generation focused on direct 3D synthesis, producing outputs such as point clouds, voxels, boundary representations, and meshes (Lambourne et al., 2021; Li et al., 2025b; Alam &Ahmed, 2024; Xu et al.; 2025; Jayaraman et al., 2022). However, these topological formats are typically too complex for engineers to easily parameterize or edit (Yu et al., 2025). To address this limitation, recent research has shifted toward program synthesis (Bhuyan et al., 2024; Jones et al., 2022; Ganeshan et al., 2023), where models output executable code (e.g., CadQuery) to construct the desired geometry (Doris et al., 2025; Kolodiazhnyi et al., 2025; Rukhovich et al., 2025). While promising, these methods often rely on post-training pipelines hindered by scarce multimodal data. This scarcity leads to brittle alignment between inputs and the resulting programs, ultimately requiring heavy manual engineering and post-processing (Guan et al., 2025; Wang et al., 2025b; Chen et al., 2025; Li et al., 2025d; Niu et al., 2026). Although some frameworks attempt to resolve these alignment issues using online reinforcement learning, they introduce computational overhead; executing CPU-bound geometric kernels within the training loop creates data-loading bottlenecks that starve GPU resources (Li et al., 2025c; Kolodiazhnyi et al., 2025). GIFT overcomes this bottleneck by decoupling exploration from training, running the geometric kernel offline, and heavily parallelizing the sampling process. Furthermore, while other recent studies use feedback-driven techniques to improve post-training (Wang et al., 2025a; Ding et al., 2026), GIFT integrates this feedback directly into inference-time compute to dynamically steer the sampling process. Inference-Time ScalingInference-Time Scaling (ITS) enhances generative capabilities by allocating additional compute at test time to produce higher-quality outputs, effectively framing generation as a guided search problem (Wang et al., 2022; Wei et al., 2022; Brown et al., 2024; Snell et al., 2024; Beeching et al., 2024; Kang et al., 2025; Dang et al., 2025). Within this framework, two primary strategies have emerged: sequential refinement techniques that iteratively improve a single output (Shinn et al., 2024; Yao et al., 2022; Jaech et al., 2024; Guo et al., 2025), and parallel approaches - such as Self-Consistency and Best-of-N sampling - that generate multiple candidates simultaneously (Wang et al., 2022; Chen et al., 2023; Brown et al., 2024; Kang et al., 2025; Amini et al., 2024). To steer this search toward optimal solutions, both methods typically rely on outcome verifiers or process rewards (Lightman et al., 2023; Cobbe et al., 2021; Puri et al., 2025; Geuter et al., 2025; Giannone et al., 2025). Particularly in code generation, execution feedback serves as a critical mechanism to scale inference (Li et al., 2025a) and boost overall performance (Li et al., 2022). GIFT builds upon these foundational concepts but focuses on amortizing the search process. By distilling the successes of expensive test-time computation directly into the model’s weights, GIFT achieves efficient, high-quality generation without the burden of added inference latency. Self-Training and Data AugmentationIterative self-training methods - such as STaR (Zelikman et al., 2022), ReST (Gul- cehre et al., 2023), and RFT (Xiong et al., 2025) - have demonstrated that models can bootstrap their own performance by training on filtered, high-quality generations. Whereas reasoning domains typically rely on logical consistency checks for this filtering, CAD generation is uniquely guided by a deterministic geometric kernel rather than sparse unit tests or learned reward models. We leverage this kernel as a dense verifier to provide exact, sample-level feedback. Furthermore, while frameworks like RFT (Xiong et al., 2025) boost performance by training exclusively on "gold" samples, they inadvertently discard the valuable learning signals embedded in near-miss failures. GIFT generalizes this approach by not only reinforcing diverse successes (via SRS) but also explicitly learning to correct failures (via FDA). By pairing rendered failure cases with their corresponding ground-truth code, we effectively transform geometric errors into a supervised signal for geometric denoising (Bsharat &Shen, 2025). Unlike standard online reinforcement learning techniques that demand complex value estimation and online sampling (Schulman et al., 2017; Guo et al., 2025), GIFT amortizes the search cost directly into the supervised policy. This approach elevates the training dataset from a static collection of successes into a dynamic curriculum of error correction. 13 Geometric Inference Feedback Tuning B. Algorithm Algorithm 1 Geometric Inference Feedback Tuning (GIFT) Input: DatasetD SFT =(c (n) , z (n) gt ) N n=1 , Base Model p θ , Budget K Parameters: τ low = 0.5, τ valid = 0.9, τ match = 0.99 Initialize: D train ←D SFT // Data: Bootstrapping via Inference-Time Scaling for each (c, z gt )∈D SFT do Sample candidatesZ K =z (k) K k=1 ∼ p θ (·|c) for each z (k) ∈Z K do Compute geometric score: s k ← IoU(z (k) , z gt ) // Soft Rejection Sampling if τ valid ≤ s k < τ match then Add diverse valid sample: D train ←D train ∪(c, z (k) ) end if // Failure-Driven Augmentation if τ low ≤ s k < τ valid then Render hard negative input: ̃ c← φ(d(z (k) )) Add robustness pair: D train ←D train ∪( ̃ c, z gt ) end if end for end for // Model: Amortization via GIFT while not converged do Sample batchB ∼D train Update θ to minimize log-likelihood objective: L(θ) =− 1 |B| P (c,z)∈B logp θ (z|c) end while 14 Geometric Inference Feedback Tuning C. Ablations C.1. Inference-Time Scaling Ablation Figure 12 extends the inference-time scaling analysis by including GIFT-FAIL alongside SFT, GIFT-REJECT, and the full GIFT model. Across all compute budgets, the full GIFT model remains the strongest configuration, indicating that output diversification and failure-driven robustness are complementary rather than redundant. Notably, GIFT-FAIL alone already yields a substantial gain over the SFT baseline, suggesting that learning from structured near-miss failures is an effective way to improve single-view Image-to-CAD generation. 12345678910 K 0.70 0.72 0.74 0.76 0.78 0.80 0.82 IoU GIFT GIFT-FAIL GIFT-REJECT SFT Figure 12. Extended inference-time scaling comparison including GIFT-FAIL. Across all compute budgets, GIFT achieves the highest IoU, while GIFT-FAIL and GIFT-REJECT each improve over the SFT baseline. The full GIFT model matches the high-compute performance of SFT with substantially less inference-time sampling. 15 Geometric Inference Feedback Tuning C.2. Model Ablation Table 6 and Figure 13 examine whether the benefits of GIFT depend strongly on the base model used for augmentation and training. Across training phases and sampler choices, the overall trend is consistent: the amortization mechanism itself remains beneficial across model variants. This suggests that GIFT is not tied to a single initialization and can be viewed as a general recipe for converting inference-time geometric feedback into improved supervised training signals. Table 6. Base-model ablation for GIFT. We compare the sampler and training backbone combinations used to generate augmented data and analyze how base-model choice affects downstream performance. Base ModelSampler QwenVL-2.5-7BCAD-Coder-7B QwenVL-2.5-3BCAD-Coder-7B CAD-Coder-7BCAD-Coder-7B 12345678910 K 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 IoU GIFT w/ QwenVL-2.5-7b GIFT w/ QwenVL-2.5-3b GIFT w/ CADCoder-7b (a) 5k steps. 12345678910 K 0.765 0.770 0.775 0.780 0.785 0.790 0.795 0.800 IoU GIFT w/ QwenVL-2.5-7b GIFT w/ QwenVL-2.5-3b GIFT w/ CADCoder-7b (b) 10k steps. 12345678910 K 0.73 0.74 0.75 0.76 0.77 0.78 0.79 IoU GIFT w/ QwenVL-2.5-7b GIFT w/ QwenVL-2.5-3b GIFT w/ CADCoder-7b (c) 15k steps. Figure 13. Base-model ablation across training phases. We compare GIFT variants bootstrapped with different base and sampler models at 5k, 10k, and 15k training steps. The benefits of GIFT persist across training progress. 16 Geometric Inference Feedback Tuning C.3. Sampling Temperature Ablation Figure 14 studies sensitivity to decoding temperature at inference time. The SFT baseline degrades more noticeably as temperature increases, whereas GIFT maintains stronger performance across the full range, especially in higher-temperature regimes. This supports the claim that GIFT broadens the model’s support over valid programs, making it less brittle to exploratory decoding. 0.10.20.30.51.0 Temperature 0.66 0.68 0.70 0.72 0.74 0.76 IOU GIFT SFT Figure 14. Sensitivity to temperature sampling for GIFT and SFT. GIFT is more robust in particular for large temperatures. 17 Geometric Inference Feedback Tuning D. Additional Experiments D.1. Out-of-Distribution Evaluation Table 7 provides a more detailed error analysis for both in-distribution and out-of-distribution evaluation. On the in-distribution split, GIFT achieves a higher valid sample rate than SFT while also reducing failed generations and OpenCASCADEexecution failures. On the out-of-distribution split, the picture is more mixed: GIFT preserves a strong valid-sample rate and lowers direct generation failures, but kernel-related failures increase, indicating that robustness to real-world imagery remains constrained by execution stability as well as prediction quality. Table 7. Valid sample rate and error analysis for GIFT and CAD-Coder-SFT on in-distribution and out-of-distribution test sets. We report pass@1 validity along with failure categories including generation failures, OpenCASCADE failures, and not-solid outputs. Valid Sample Rate (%)Error Analysis (%) MethodSplitpass@1Failed GenFailed OCCNot Solids GIFTin-distribution99.060.200.380.35 out-of-distribution96.750.602.450.20 SFTin-distribution98.750.340.600.31 out-of-distribution97.601.181.180.05 Figure 15 presents a preliminary out-of-distribution scaling analysis on 400 real-world images (Doris et al., 2025). Although absolute IoU is substantially lower than on the standard test set, GIFT maintains a clear advantage over SFT across compute budgets, suggesting that the benefits of amortized geometric feedback transfer beyond the training distribution. At the same time, the reduced OOD performance highlights that further work is needed to improve visual robustness and compilation reliability under more realistic image conditions. 12345678910 K 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 IoU GIFT OOD SFT OOD Figure 15. Preliminary out-of-distribution evaluation using a set of 400 real-world images, based on the data split provided by (Doris et al., 2025). The results show that GIFT effectively leverages inference-time compute to handle challenging, unseen inputs. 18 Geometric Inference Feedback Tuning D.2. Failure Handling Table 8 contextualizes our results against stronger multimodal and specialized systems (Kolodiazhnyi et al., 2025), including settings with and without failed generations. The comparison highlights two points. First, failure handling materially affects reported mean IoU, making median IoU a useful complementary statistic for program-generation systems. Second, despite relying only on a single-view image and a general-purpose VLM backbone, CAD-Coder-GIFT closes a meaningful portion of the gap to specialized multimodal pipelines. Table 8. Comparison with recent multimodal and specialized CAD-generation systems. PC denotes point clouds, IMG multi-view images, and IMG-s single-view images; w/ f includes failed generations, while w/o f excludes them. Reporting both mean and median IoU highlights the sensitivity of average performance to failed executions. ModalityIoU (mean)IoU (median) cadrille-RL (w/o f)PC0.9120.974 cadrille-RL (w/o f)PC,IMG0.9200.978 cadrille-RL (w/ f)PC0.8200.966 cadrille-RL (w/ f)PC, IMG0.8270.972 CAD-Coder-SFT (w/ f)IMG-s0.6980.803 CAD-Coder-GIFT (w/ f)IMG-s0.7820.948 D.3. Performance Metrics and Task Complexity Figure 16 refines the intrinsic robustness analysis by separating complexity into operation-count and token-count views. Across both measures, GIFT improves median and mean IoU while increasing the fraction of successfully solved problems, especially on more complex examples. This supports the interpretation that GIFT does not merely improve easy cases, but shifts the model toward more reliable geometric reasoning on harder synthesis tasks. Figure 17 analyzes the distribution of problem complexity in both ground-truth and generated programs. The comparison suggests that the gains from GIFT are not explained simply by producing shorter or structurally simpler programs. Instead, the model continues to generate programs with complexity profiles similar to the target distribution while achieving higher geometric fidelity, indicating better alignment rather than trivial simplification. 19 Geometric Inference Feedback Tuning Method IoU Median Mean 0.846 0.695 0.905 0.742 0.948 0.781 SFT GIFT-REJECT GIFT (a) Accuracy. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Problems Solved SFT GIFT-REJECT GIFT +31.4% +53.8% (b) Ratio Problems Solved. <1515-25>25 Task Complexity - Operations 0.5 0.6 0.7 0.8 0.9 IOU SFT GIFT-REJECT GIFT (c) Performance vs Complexity (Operations). <300300-400>500 Task Complexity - Tokens 0.5 0.6 0.7 0.8 0.9 IOU SFT GIFT-REJECT GIFT (d) Performance vs Complexity (Tokens). Figure 16. Performance metrics under different data-augmentation strategies. We evaluate Top-K (K = 10) generations filtered by geometric validity (IoU≥ 0.9against the ground truth) and compare accuracy, solved-problem rate, and performance as a function of task complexity. GIFT improves both geometric fidelity and robustness, with the largest gains appearing on more complex problems. 20 Geometric Inference Feedback Tuning SFTGIFT-REJECTGIFT 10 15 20 25 30 35 40 Number of Operations (Ground Truth) (a) Operations (Ground Truth). SFTGIFT-REJECTGIFT 200 300 400 500 600 700 800 900 1000 Number of Tokens (Ground Truth) (b) Tokens (Ground Truth). SFTGIFT-REJECTGIFT 10 15 20 25 30 35 40 Number of Operations (Generated) (c) Operations (Generated). SFTGIFT-REJECTGIFT 200 300 400 500 600 700 800 900 Number of Tokens (Generated) (d) Tokens (Generated). 0102030405060 Operations (Generated) 0.00 0.02 0.04 0.06 0.08 Density SFT GIFT-REJECT GIFT (e) Mean Operations (Generated). 025050075010001250 Tokens (Generated) 0.000 0.001 0.002 0.003 0.004 Density SFT GIFT-REJECT GIFT (f) Mean Tokens (Generated). Figure 17. Complexity statistics for ground-truth and generated programs with high-fidelity. We compare the distributions of operation counts and token lengths across SFT, GIFT-REJECT, and GIFT. The results show that GIFT improves alignment with valid target structures. 21 Geometric Inference Feedback Tuning E. Can Frontier Models Zero-Shot Image-to-CAD? Table 9 compares GIFT against a frontier general-purpose multimodal model in a zero-shot Image-to-CAD setting. The results show that foundation models exhibit nontrivial geometric competence, especially with higher-resolution inputs, but still trail a specialized domain-adapted system by a large margin. This reinforces the value of targeted geometric supervision and domain-specific amortization even in the era of very capable generalist VLMs. Table 9. Mean and median IoU on a subset of the GenCAD test set for zero-shot Gemini 3.0 Pro and the specialized CAD-Coder-GIFT model. Results are shown for different input resolutions to assess the sensitivity of frontier multimodal models to visual detail. ModelModeInput ResIoU (mean)IoU (median) Gemini-3-PROZero-ShotLow0.2000.141 Gemini-3-PROZero-ShotHigh0.5400.560 CAD-CoderGIFT-0.7820.948 To assess state-of-the-art multimodal capabilities in engineering design, we evaluated Gemini 3.0 Pro (Team et al., 2023) on zero-shot Image-to-CAD generation. As shown in Table 9, performance is heavily dependent on input resolution, with high-resolution inputs more than doubling mean IoU. While this indicates a remarkable emergent geometric understanding in general-purpose foundation models, they still lag behind specialized systems. Our domain-specific CAD-Coder with GIFT significantly outperforms the frontier model, demonstrating that smaller, specialized architectures remain superior for high-fidelity CAD program synthesis. 22 Geometric Inference Feedback Tuning F. Dataset Generation 0.900.920.940.960.98 IoU 0 5 10 15 20 Density Figure 18. Distribution of Top-1 samples with IoU > 0.9. Sampling Strategy Our objective is to curate a diverse dataset of CadQuery programs for single images, effec- tively mimicking the multiple valid reasoning paths exhibited by large language models. To achieve this, we employ QwenVL-2.5-7B-CADCoderas our primary sampler. We strictly utilize the existing training set as source material, leveraging ground truth STEP files as the exclusive source of geometric feedback.The dataset is constructed via a multi-stage pipeline that scales candidate generation across five distinct computational budgets: N ∈8, 16, 32, 64, 128. Starting with a base pool of 80,000 training images, we sample subsets of 10,000 (increasing to 40,000 for theN = 32 budget). To maximize semantic diversity, we implement an inverse scaling strategy across 29 hyperparameter configurations. As detailed in Table 10, lower compute budgets utilize broader temperature ranges (e.g.,T ∈0.2, 0.4, 0.6) to encourage exploration, whereas higher budgets prioritize precision through strict, low-temperature sampling (T = 0.2). Table 10. Dataset budget mix and sampling hyperparameter configurations used during data generation. The Samples column reports the selected subset size retained for each compute budget after top-10% filtering. BudgetInputsSamples(T , p) N = 810,00010,000 T = 0.2 : p∈0.7, 0.8, 0.9, 1.0 T = 0.4 : p∈0.7, 0.8, 0.9, 1.0 T = 0.6 : p∈0.8, 0.9, 1.0 N = 1610,00020,000 T = 0.2 : p∈0.7, 0.8, 0.9, 1.0 T = 0.4 : p∈0.8, 0.9, 1.0 N = 3240,000120,000 T = 0.2 : p∈0.7, 0.8, 0.9, 1.0 T = 0.4 : p∈0.9, 1.0 N = 6410,00060,000 T = 0.2 : p∈0.8, 0.9, 1.0 N = 12810,000120,000 T = 0.2 : p∈0.9, 1.0 23 Geometric Inference Feedback Tuning Selection StrategyFrom approximately 1 million generated raw samples, we compute the Intersection over Union (IoU) against ground truth scripts to partition the data into three distinct splits. TheFULLsplit retains the top 10% of successful generations per input (whereIoU > 0.5). TheFAILsplit isolates failure modes by selecting the highest-scoring candidate for inputs where satisfactory reconstruction failed (IoU < 0.9). Finally, we construct the Soft Rejection Sampling (SRS) set for high-quality fine-tuning. This split combines the original ground truth data with the single best generated candidate (Top-1) falling within the range0.9 < IoU < 0.99(excluding exact duplicates). Oversampling While selecting the best ofKgenerations is generally effective, it relies on the assumption that a valid candidate exists within the sample pool. Our analysis indicates that for a significant portion of the training set, simply increasing sampling frequency fails to yield high-IoU results. To mitigate this, we leverage geometric feedback to identify these persistent failures and selectively augment the dataset with these hard samples. 0.00.20.40.60.81.0 IoU 0 5000 10000 15000 20000 25000 30000 35000 40000 Frequency (a) Before balancing. 0.00.20.40.60.81.0 IoU 0 2500 5000 7500 10000 12500 15000 17500 Frequency (b) After balancing. Figure 19. IoU distribution of sampled programs before and after balancing. Balancing reduces over-representation of the densest score ranges and produces a more even distribution of training examples across quality levels, improving the usefulness of both SRS and FDA data. 24 Geometric Inference Feedback Tuning G. Amortizing Inference-Time Augmentation: Gradients In this section, we analyze the gradients of the GIFT objective function and establish the theoretical connection between our rejection-sampling approach and standard policy gradient methods. The Reinforcement Learning Perspective Ideally, we aim to maximize the expected geometric validity (IoU) of the generated programs. Let J (θ) be the expected reward under the policy p θ : J (θ) =E c∼q D ,z∼p θ (·|c) [r(z, z gt )],(6) where the rewardr(z, z gt ) = f (z)is the Intersection over Union (IoU) defined in the Method. Maximizing this objective via gradient ascent yields the standard REINFORCE policy gradient: ∇ θ J (θ) =E c,z [f (z)∇ θ logp θ (z|c)].(7) In standard online RL (e.g., PPO), this expectation is approximated by sampling batches from the current policyπ θ during training. However, this is computationally prohibitive for CAD synthesis because computingf (z)requires executing an expensive geometric kernel for every step. G.1. The GIFT Approximation GIFT bypasses online sampling by approximating the expectation using a static, high-quality dataset collected via Inference- Time Scaling (ITS). We treat the sample selection process as an importance sampling step where the weights are binary (hard rejection). SRS Gradient (Diversity)The SRS component effectively performs Reward-Weighted Regression with a hard threshold. Instead of weighting every sample by its scalar rewardf (z), we define a binary weightw srs (z) = 1[τ valid ≤ f (z) < τ match ]. The gradient for the SRS objective provided in Eq. 4 is: ∇ θ F SRS =E (c,z)∼D SRS [∇ θ logp θ (z|c)].(8) Substituting the definition ofD SRS , this is equivalent to a Monte-Carlo approximation of the policy gradient where samples with low reward are zeroed out: ∇ θ F SRS ≈ N X n=1 K X k=1 w srs (z (k) )∇ θ logp θ (z (k) |c (n) ).(9) This formulation stabilizes training by treating the generated programsz (k) as fixed "pseudo-ground-truths," converting the unstable RL problem into a standard supervised maximum likelihood estimation (MLE) problem. FDA Gradient (Robustness)The FDA component introduces a distinct gradient signal. Unlike SRS, which optimizes the likelihood of the generated sample z, FDA optimizes the likelihood of the ground truth z gt conditioned on a noisy input ̃ c. The objective is a supervised denoising loss: F FDA =E ( ̃ c,z gt )∼D FDA [logp θ (z gt | ̃ c)].(10) The gradient is straightforward: ∇ θ F FDA = N X n=1 K X k=1 w fda (z (k) )∇ θ logp θ (z (n) gt |φ(d(sg[z (k) ]))).(11) Here, the gradient signal does not encourage the production of the failed samplez (k) . Instead, it updates the visual encoder and language decoder to be invariant to the geometric perturbations present in ̃ c = φ(d(z (k) )), pulling the distribution back towards the mode z gt . 25 Geometric Inference Feedback Tuning Augmented Gradient Update Combining the Base (SFT), Diversity (SRS), and Robustness (FDA) terms, the final parameter update at each step is: ∆θ ∝ X n ∇ θ logp(z (n) gt |c (n) ) | z SFT: Grounding + X n,k w (k) srs ∇ θ logp(z (k) |c (n) ) | z SRS: Diversity + X n,k w (k) fda ∇ θ logp(z (n) gt | ̃ c (k) ) |z FDA: Robustness (12) This formulation allows GIFT to amortize the cost of search into the model weights offline, avoiding the variance and computational cost of online policy gradient estimation. 26 Geometric Inference Feedback Tuning H. Visualizations (a)(b)(c) (d)(e)(f) (g)(h)(i) Figure 20. Rendered examples of generated CAD programs with intermediate IoU quality (IoU > 0.5andIoU < 0.9). These visualizations show how geometrically imperfect but executable programs can be projected back into the image domain and reused as synthetic inputs for Failure-Driven Augmentation. 27 Geometric Inference Feedback Tuning Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Ground Truth CAD Input Image Generated CAD 0200400 0 100 200 300 400 Augmented Image Figure 21. Examples of low-IoU but executable generations used for Failure-Driven Augmentation. The rendered failures provide structured hard negatives that train the model to recover the original ground-truth program from imperfect visual geometry. 28 Geometric Inference Feedback Tuning Generate cadquery code for this image Image-to-CAD SFT IoU = 1 (a) SFT workflow description Image-to-CAD GIFT (b) GIFT workflow description Figure 22. Workflow comparison between standard SFT and GIFT. In the SFT pipeline, each input image is paired with a single ground-truth program. In GIFT, multiple sampled programs are geometrically verified, and both high-quality alternatives and structured failures are converted into additional supervised training signals. 29 Geometric Inference Feedback Tuning Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Figure 23. Example of high IoU CAD generations used for SRS augmentation. 30 Geometric Inference Feedback Tuning Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Figure 24. Example of high IoU CAD generations used for SRS augmentation. 31 Geometric Inference Feedback Tuning Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Ground Truth CADGenerated CADGround Truth CADGenerated CADGround Truth CADGenerated CAD Figure 25. Example of high IoU CAD generations used for SRS augmentation. 32 Geometric Inference Feedback Tuning I. Details Table 11. Experimental setup and implementation details for training, inference-time scaling, and GIFT-specific augmentation. We summarize model backbones, dataset sizes, sampling budgets, filtering thresholds, optimization settings, and hardware. HyperparameterValue Model Architecture Base ModelQwen-VL-2.5-7B-Instruct/Qwen-VL-2.5-3B-Instruct Parameter Count7B/3B Datasets Source DatasetGenCAD-Code / DeepCAD Training Size (Original SFT)163k Augmented Dataset Size370k IN Test Set Size7355 OOD Test Set Size400 Inference-Time Scaling (Data Generation) Sampling Budgets (N )8, 16, 32, 64, 128 Sampling Temperatures (T )0.2, 0.4, 0.6 Top-p values0.7, 0.8, 0.9, 1.0 Sampler ModelQwenVL-2.5-7B-CADCoder GIFT Configuration SRS Validity Range (τ valid )0.9≤ IoU < 0.99 FDA Range (τ noise )0.5≤ IoU < 0.9 Geometric KernelOpenCASCADE / CadQuery Training Optimization OptimizerAdamW Learning Rate2e− 5 LR SchedulerCosine Decay Batch Size / GPU4 Training Epochs10 PrecisionBF16 Hardware8x A100 80GB 33