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CADFather: Autonomous CAD Reconstruction through Coordinated Tool Use
Gennadiy Savrasov, Maksim Elistratov, Nikita Gavrilov, Albert Garifullin, Oleg Pavlov, Soslan Kabisov, Vladimir Frolov, Anton Konushin, Andrey Kuznetsov, Dmitrii Zhemchuzhnikov
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
Last extracted: 10/8/2026, 6:56:26 AM
Summary
The paper introduces CADFather, an autonomous agentic system for reconstructing editable parametric CAD models from 3D meshes. It employs a vision-language assistant to coordinate complementary tools—learned proposal generation, algorithmic proposal generation, and numerical parameter optimization—within a search process that maintains a pool of alternative candidate programs. The system evaluates reconstruction quality and validity across multiple datasets without additional training of the core models.
Entities (14)
Relation Signals (11)
Gennadiy Savrasov → affiliatedwith → Lomonosov Moscow State University
confidence 95% · Gennadiy Savrasov 1 ... 1 Lomonosov Moscow State University
CADFather → usestool → Algorithmic Proposal Generation
confidence 95% · The tools comprise learned proposal generation, algorithmic proposal generation, and parameter optimization.
CADFather → usestool → Parameter Optimization
confidence 95% · The tools comprise learned proposal generation, algorithmic proposal generation, and parameter optimization.
CADFather → usestool → Learned Proposal Generation
confidence 95% · The tools comprise learned proposal generation, algorithmic proposal generation, and parameter optimization.
CADFather → evaluatedon → CADBench
confidence 90% · ...as well as on CADENA-Bench, CADBench, and BenchCAD.
CADFather → evaluatedon → BenchCAD
confidence 90% · ...as well as on CADENA-Bench, CADBench, and BenchCAD.
CADFather → evaluatedon → MCB
confidence 90% · We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets...
CADFather → evaluatedon → DeepCAD
confidence 90% · We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets...
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Abstract
Abstract:Reconstructing an editable CAD model from a 3D shape remains a challenging engineering task. Existing methods can propose CAD operations, but no single source of proposals works equally well across different part geometries and stages of reconstruction. We introduce CADFather, an autonomous agentic system that coordinates complementary tools to recover parametric CAD programs from 3D meshes. A vision-language assistant inspects renders of the target and intermediate reconstructions, then decides which candidate CAD programs to extend, which tools to invoke, how many proposals to generate, and when to finish. Learned and algorithmic tools propose CAD operations, while numerical optimization refines the parameters of existing programs. Proposed or refined programs are executed and evaluated to provide feedback for subsequent decisions. The agent maintains alternative candidate programs for each target part and preserves the best valid result throughout reconstruction. CADFather uses pretrained generation and assistant models without additional training. We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets, as well as on CADENA-Bench, CADBench, and BenchCAD. We additionally analyze computational cost and the trade-off between cost and reconstruction quality.
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- Source: https://arxiv.org/abs/2610.09127v1
- Canonical: https://arxiv.org/abs/2610.09127v1
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CADFATHER: AUTONOMOUS CAD RECONSTRUCTION THROUGH COORDINATED TOOL USE A PREPRINT Gennadiy Savrasov 1 Maksim Elistratov 1 Nikita Gavrilov 1 Albert Garifullin 1 Oleg Pavlov 1 Soslan Kabisov 1 Vladimir Frolov 1 Anton Konushin 1 Andrey Kuznetsov 2,3 Dmitrii Zhemchuzhnikov 1∗ 1 Lomonosov Moscow State University; 2 Innopolis University; 3 FusionBrain Lab ABSTRACT Reconstructing an editable CAD model from a 3D shape remains a challenging engineering task. Existing methods can propose CAD operations, but no single source of proposals works equally well across different part geometries and stages of reconstruction. We introduce CADFather, an autonomous agentic system that coordinates complementary tools to recover parametric CAD pro- grams from 3D meshes. A vision-language assistant inspects renders of the target and intermediate reconstructions, then decides which candidate CAD programs to extend, which tools to invoke, how many proposals to generate, and when to finish. Learned and algorithmic tools propose CAD operations, while numerical optimization refines the parameters of existing programs. Proposed or refined programs are executed and evaluated to provide feedback for subsequent decisions. The agent maintains alternative candidate programs for each target part and preserves the best valid result throughout reconstruction. CADFather uses pretrained generation and assistant models without additional training. We evaluate reconstruction quality and execution validity on the full DeepCAD, Fusion360, and MCB test sets, as well as on CADENA-Bench, CADBench, and BenchCAD. We additionally analyze computational cost and the trade-off between cost and reconstruction quality. Code repository: https://github.com/kulibinai/CADFather. Keywords CAD reverse engineering· vision-language agents· parametric modeling· tool-using agents 1 Introduction A mesh describes a shape, but it does not by itself encode the modeling operations and feature parameters used to construct that shape. Recovering an executable CAD program makes these quantities available for inspection and modification. For example, a suitable construction program can expose a bore diameter or wall thickness as an editable parameter. This capability is valuable when a component is available only as a scan, a legacy mesh, or a model without its construction history. The reconstruction must be executable, structurally coherent, and useful as an editable model. Recent work has explored several approaches to CAD reconstruction. Some methods adopt a learned approach, fine-tuning language or vision-language models to predict CAD code from geometric observations, as in CAD-Recode, cadrille, CADEvolve, CADReasoner, and CADENA [Rukhovich et al., 2025, Kolodiazhnyi et al., 2025, Elistratov et al., 2026, Kabisov et al., 2026a,b]. Within this class, CAD-Recode, cadrille, and the reconstruction model trained with CADEvolve generate complete programs in a single pass. CADReasoner and CADENA instead reconstruct iteratively: CADReasoner revises complete programs using feedback on discrepancies with the target, while CADENA extends ∗ Corresponding author: zhemchuzhnikovds@my.msu.ru. arXiv:2610.09127v1 [cs.AI] 6 Oct 2026 CADFatherA PREPRINT a partial program one operation at a time using renders of the target and current reconstruction. CADFit follows an algorithmic approach, reconstructing the target through geometric fitting and validation of candidate operations within an optimization-based search [Nehme et al., 2026]. Numerical parameter optimization adjusts an existing program while retaining its operation structure [Cascaval et al., 2022, Yuan et al., 2024]. These approaches offer complementary ways to improve a reconstruction. A learned model can propose plausible modeling operations, but its proposals may miss a feature or use inaccurate dimensions. Algorithmic construction provides an additional source of operations derived directly from the target geometry, while parameter optimization can refine the dimensions of an otherwise suitable program. Combining these capabilities allows the system to explore alternative constructions and improve the fit of existing ones. The useful action depends on the current reconstruction: it may need another operation, parameter refinement, or a return to an earlier candidate. This motivates a process that selects both the candidate to develop and the tool to apply using feedback from the executed geometry. We introduce CADFather, which maintains a pool of alternative CAD programs and uses a vision-language assistant to guide their reconstruction. At each step, the assistant inspects target and candidate renders, geometric scores, available actions, and the history of executed requests. It then selects candidates to extend or refine, chooses tools, specifies how many learned proposals to sample, or ends reconstruction. The tools comprise learned proposal generation, algorithmic proposal generation, and parameter optimization. Learned proposals come from a pretrained operation generator; algorithmic proposals are constructed from geometry without a learned proposal model. Parameter optimization refines an existing program. Each proposed program is executed and measured. The assistant then inspects its rendered geometry and decides whether to accept it into the candidate pool. Earlier candidates remain available, and the system preserves the best valid result throughout the search. CAD-Assistant and IterCAD already show how visual agents can use executable CAD environments and inspect the outcomes of their actions [Mallis et al., 2025, Hu et al., 2026]. CADFather applies this interaction pattern to a pool of alternative mesh reconstructions, with specialized proposal and refinement tools. Our focus is the integration of these capabilities in a shared representation and search process. Neither the operation generator nor the assistant requires additional training. Our contributions are: •a mesh-to-CAD reconstruction agent that uses visual and execution feedback to select candidate programs, choose reconstruction tools, and allocate learned proposal samples; •a shared reconstruction framework combining learned proposals, algorithmic proposals, parameter optimiza- tion, and persistent retention of the best valid result; •an evaluation on six datasets, with published-method comparisons and ablations removing algorithmic proposals, parameter optimization, or both. The experiments assess geometric fidelity, validity, and selected measures of computational cost. They evaluate the complete system and the contribution of making the different tools available during reconstruction. 2 Related Work Generative CAD modeling. Many learning-based CAD methods generate sequences of construction operations and their parameters, rather than only meshes or point clouds. DeepCAD learns distributions over sketch–extrude construction sequences [Wu et al., 2021], while the Fusion360 Gallery provides human modeling histories and an environment for programmatic construction [Willis et al., 2021]. SkexGen separates aspects of topology and geometry through disentangled codebooks for construction-sequence generation [Xu et al., 2022]. A complementary line models the sketches underlying these operations: SketchGen and Vitruvion generate parametric sketches with constraints [Para et al., 2021, Seff et al., 2022], while CadVLM incorporates visual and language inputs for sketch generation [Wu et al., 2024]. These methods establish representations and generative models for CAD construction, but generating a plausible design is distinct from recovering a program for a specified target mesh. CADFather reconstructs a specified target mesh using existing CAD modeling capabilities within an agent. Geometric reconstruction and executable CAD programs.CAD reconstruction methods differ in the representation they recover. ComplexGen reconstructs boundary representations through their geometric and topological structure [Guo et al., 2022]; SolidGen and BrepGen study direct generation of boundary representations [Jayaraman et al., 2023, Xu et al., 2024]. Constructive solid geometry methods such as CSGNet, UCSG-Net, and CAPRI-Net describe shapes through primitive combinations [Sharma et al., 2022, Kania et al., 2020, Yu et al., 2022]. Point2Cyl recovers extrusion cylinders from point clouds, while ExtrudeNet and SECAD-Net learn inverse sketch-and-extrude representations [Uy 2 CADFatherA PREPRINT et al., 2022, Ren et al., 2022, Li et al., 2023]. These approaches recover structured geometry, although their outputs need not provide general-purpose CAD code with an explicit modeling sequence. Methods targeting executable programs include CAD-Recode, which maps point clouds to CadQuery code [Rukhovich et al., 2025], and cadrille, which supports multimodal reconstruction and uses reinforcement learning with geometric rewards [Kolodiazhnyi et al., 2025]. CAD-Coder generates CAD code from visual inputs [Doris et al., 2025], while CADEvolve develops training data through CAD program evolution [Elistratov et al., 2026]. CADFather targets executable construction programs and combines learning-based operation generation with geometry-based operation proposals through a common tool interface. Iterative and stepwise CAD reconstruction.Executing intermediate programs makes their resulting geometry avail- able to guide subsequent reconstruction. Zone-graph methods search over CAD modeling sequences [Xu et al., 2021], and CADFit combines incremental operation construction with hybrid optimization against the target mesh [Nehme et al., 2026]. CADReasoner uses geometric discrepancies to iteratively edit complete CAD programs [Kabisov et al., 2026a]. CADENA adopts a different prediction unit: it executes a partial program, renders its geometry together with the target, and generates one additional operation [Kabisov et al., 2026b]. SOV-CAD also investigates stepwise reconstruction with orthographic visual feedback, using a Decision Transformer formulation [Feng et al., 2026]. These approaches differ in what they predict and how they use intermediate geometry: some revise complete programs, while others construct them operation by operation. CADFather builds on the latter setting but makes tool selection a separate decision of the visual assistant. At each decision step, it chooses which candidate CAD program to continue, whether to request learned or algorithmic proposals, how many learned proposals to sample, or whether the current candidate is ready for parameter refinement or completion. Parameter optimization in CAD programs.Numerical refinement can adjust the geometry represented by a program without changing its operation structure. Cascaval et al. [2022] introduce a differentiable CAD language and formulate direct geometric edits as constrained optimization of program parameters. Their system seeks parameter updates that satisfy editing objectives while preserving program validity, rather than reconstructing an unknown modeling sequence. DiffCSG [Yuan et al., 2024] enables differentiable rasterization of constructive solid geometry, supporting optimization of primitive parameters for direct and image-based editing with a prescribed discrete structure. These works distinguish continuous parameter refinement from the selection of modeling operations. CADFather exposes parameter optimization as a separate tool: the assistant decides when an existing candidate should be refined rather than extended or replaced by an alternative proposal. We do not introduce a new numerical optimizer. Tool-using CAD agents. Agentic systems make the selection and execution of modeling actions explicit. CAD- Assistant uses a vision-language planner with CAD-specific tools and a FreeCAD execution environment, adapting its actions to the evolving design state [Mallis et al., 2025]. Its tools include rendering and cross-section extraction, allowing the planner to obtain additional observations rather than relying only on the initial input. IterCAD formulates visually grounded generation and editing as multimodal interaction with an executable sandbox [Hu et al., 2026]. ToolCAD studies reinforcement learning for tool-using language models in text-to-CAD generation [Gong et al., 2026], while COSMO-Agent investigates tool orchestration across modeling, simulation, and optimization [Deng et al., 2026]. CAD-Assistant already establishes vision-language planning with CAD tools and execution feedback; tool use alone is not our distinction. CADFather focuses on reconstructing an executable program for a given target mesh while maintaining alternative candidate CAD programs for that part. Its visual assistant uses intermediate renders and geometric evaluation to choose both a candidate to continue and a specialized tool to apply. This couples target-conditioned tool choice with search over alternative reconstruction branches, rather than relying on a fixed operation source or repeatedly editing a single program. 3 Method 3.1 Problem Formulation and System Overview Given a target meshM ⋆ , CADFather seeks an executable CAD programpwhose resulting geometryE (p)matches the target. For learned prediction of CAD operations, we use CADENA-RL [Kabisov et al., 2026b]. Candidate programs therefore follow CADENA’s CadQuery-based DSL, in which each line specifies a modeling operation that produces a buildable and renderable solid. All tools produce programs in this representation, so a candidate generated by one tool can subsequently be extended or refined using another. For each target part, the system maintains alternative candidate programsp i and their evaluation results. Programs that pass validation and visual acceptance become candidates for further reconstruction; rejected proposals cannot be selected for extension. 3 CADFatherA PREPRINT INPUT VLM ASSISTANT Qwen3.8-27B TOOLS Target mesh Input Target; top 12 candidates by score + best/root; renders, scores, history Output One or more actions, or finish Action: candidate, tool, number of proposals Learned model generate proposals with a learned model Algorithmic approach generate proposals with a det. algorithm* Parameter optimization generate proposals from an existing program EXECUTION + VALIDATION - Build proposed programs - Validate and deduplicate - Render and score valid results - Accept valid proposals as candidates FINAL CAD PROGRAM + MESH CANDIDATE POOL Candidate A Tool: Learned IoU: 0.861 GMS: 0.544 Candidate B Tool: Optimization IoU: 0.915 GMS: 0.537 Candidate C Tool: Algorithmic IoU: 0.238 GMS: 0.174 Candidate D Tool: Learned IoU: 0.901 GMS: 0.538 actionproposals candidate renders + scores accepted candidates (pool size varies) finish Figure 1: CADFather overview. Given a target mesh and feedback from existing CAD candidates, the visual assistant selects candidate programs to continue, tools to apply, and the number of proposals to generate. Learned and algorithmic proposals create alternative continuations, while parameter optimization refines existing candidates. The resulting programs are executed and evaluated, and the assistant visually accepts or rejects them before pool admission. Their renders and scores inform subsequent decisions. * In the figures, “stepwise” denotes learned proposals, and “deterministic” or “det” denotes algorithmic proposals. At each decision step, the vision-language assistant inspects the target and the current candidates, then chooses which candidate programs to continue, which generation or refinement tools to invoke, how many proposals to request, or whether to finish. The learned and algorithmic proposal tools offer alternative next operations, while the refinement tool, parameter optimization, adjusts an existing program without adding an operation. The agent’s execution component runs the resulting programs, validates their geometry, evaluates candidates, manages the search budget, and preserves the best valid result independently of the assistant’s current choices. The generation and assistant models require no additional training. Figure 1 summarizes this loop. 3.2 Candidate Pool Each candidate records its identifier, parent, source tool, program, generated mesh, number of CAD operations, validity, and measurements. The root represents an empty program. Extending a candidate creates a child rather than modifying its stored history. Numerical optimization may change existing parameters and is therefore distinguished from an appended CAD operation. The pool retains candidates from earlier decision steps. The assistant is not restricted to the latest generation: it can revisit an earlier valid CAD program or request a different first operation from the root, provided the corresponding actions are available. Code-level deduplication prevents an identical program from creating a new pool entry. This is textual deduplication, not a guarantee of geometric uniqueness. At each decision step, the assistant receives a bounded table summarizing selected candidates from the pool, rather than the entire pool. Only candidates that built, are watertight, and still admit a legal action are listed. Up to twelve candidates are selected in descending order of score (Eq. 2). The protected best and the empty start are also shown if they are not among those selected. Each row gives the candidate identifier, the tool that produced it, its operation count, a status mark (start or best), its score with the separate volume and surface metrics (IoU and GMS, Section 3.5), the score of the first operation of its chain, and the tools that may still be applied to it. The first-operation score helps the assistant judge whether to continue a branch or request an alternative first operation from the empty program. A low initial score is a warning signal, not a bound on the quality that later operations can achieve. A tool that is exhausted on a candidate, or does not apply to it, disappears from that row; a candidate absent from the table cannot be referenced in that step. 4 CADFatherA PREPRINT Input of step 3 Rules (same at every step) Reconstruct the target as a CAD program. Score = mean of IoU and GMS; the best candidate at the end is the answer. Tools: stepwise append one generated operation det next 4 deterministic proposals optimize tune the numbers of a program Answer: one sentence, then up to 4 act calls, or finish(shape | stalled). Transcript of steps 1-2 Step 1 “start from the empty root [...] and also kick off det” executed: stepwise(c0, n=8), det(c0) result: c1-c4 open shells; best c5, score 0.165 Step 2 “[...] append operations to c5 to add the connecting posts” executed: stepwise(c5, n=8), det(c5) result: best c13, score 0.469 Renders Target c13 best so far c5 parent of c13 Candidate table (6 of 10 rows) id from ops score IoU GMS tools c13 det 2 0.469 0.486 0.452 stepwise, det c9 step 2 0.390 0.454 0.326 stepwise, det, opt c10 det 2 0.330 0.394 0.265 stepwise, det, opt ... c5 det 1 0.165 0.197 0.133 stepwise, det, opt c0 root 0 - - - stepwise, det Assistant answer “[...] the target needs two parallel posts joining the plates, so I'l append operations to c13 to add the second post, and also try det for an alternative.” act(stepwise, c13, n=8) act(det, c13) Executed stepwise(c13, n=8) → c14, c15 det(c13) → c16-c19 c15, new best IoU 0.710 GMS 0.620 added to the transcript of step 4 Figure 2: One assistant decision step: step 3 of the trajectory in Fig. 3 (MCB chain link). The best candidate c13 has one plate and one post, while the target has two of each. The assistant continues c13 with learned proposal generation and algorithmic proposals; learned proposal generation adds the second post (c15), and the results of both calls enter the transcript of the next step. Abridged from the logged prompt and answer: the rules are paraphrased, the transcript and the rationale are excerpts, the table shows 5 of 10 rows, det denotes algorithmic proposals, and one of four rendered views is shown. 3.3 Assistant Decision Step A decision step is made for the whole part, not for each candidate: in one step the assistant sees the entire candidate table and may act on several candidates at once. Its input has four parts. The first is a rule description that is the same for every step and every part: the task, the objective, the available tools with their approximate cost, and the answer format. The second is a transcript of the reconstruction so far. For every previous step, it records the assistant’s one-sentence rationale and the actions the agent actually executed: requests for unavailable actions are dropped, and sample counts are reduced to fit the remaining budget. Recording executed rather than requested actions keeps the transcript consistent with the candidates that actually exist in the pool. The third part is a set of renders, described below, and the fourth is the candidate table (Section 3.2). From this input the assistant decides whether to sample further operations with the learned generation model, request algorithmic proposals, refine an existing program, or finish the part. Figure 2 shows one complete step. The renders do not show every candidate, only the target and the current state of the search. The render of the target is the same on every step. Once a candidate has been built, the prompt also shows two candidates: the best one so far and the best one produced by the previous step. If the previous step itself produced the new best, the second image shows its parent instead, so that the assistant sees the effect of the last operation; if the previous step produced no valid candidate, only the best is shown. Each image is labeled with the id from the candidate table, its operation count, and its score. Renders from earlier steps are not kept in the prompt. Visual acceptance additionally uses renders of newly proposed programs (Section 3.5). The assistant answers through function calls. It first writes one short sentence stating what it pursues in this step; this sentence, unlike any further reasoning, is carried into the transcript. It then issues up to fouractcalls, each naming a tool and a candidate from the table, and for learned proposal generation a sample countn. Afinishcall ends the whole part with one of two reasons (Section 3.6); it may accompany act calls, in which case the step is the last one. 3.4 Reconstruction Tools Learned proposal generation. For a parent programp i , the learned proposal generation tool producesnnext- operation proposals in a single request. Each accepted proposal forms a child program by continuing the selected parent’s program. The countndenotes generated alternatives, notnsequential operations within one child. The assistant choosesnup to a limit printed in the candidate table: the smaller of a fixed per-call cap and the generator samples still left in the part’s budget. The limit applies to each call; when several learned calls in one step together exceed the remaining budget, the execution component reduces n of the later ones or drops them. 5 CADFatherA PREPRINT Algorithmic proposal generation. The algorithmic proposal tool constructs CAD operations through geometric fitting to the target mesh, without a learned generation model. It is conceptually similar to CADFit [Nehme et al., 2026], but uses a separate implementation. The assistant decides when and on which candidate to call it. The tool has two entry points. On the empty start, the tool proposes a first operation from the target mesh alone. If the part is a body of revolution, the first proposal revolves its profile. The tool then looks for extrusions: it cuts the target with planes, takes each cross-section as a sketch, and finds the depth over which this sketch follows the target surface. Extrusions that add little to the overlap with the target are dropped, so each remaining one matches a separate feature of the part. On an existing candidate, the tool proposes the next operation; we call these warm proposals. It compares the candidate with the target and finds two regions: material that is missing and material that is extra. The same extrusion search runs on each region. Missing material gives extrusions to add, and extra material gives cuts. The proposals form a ranked list. Unlike learned proposal generation, the assistant does not choose how many proposals to take: each call returns the next four proposals from the list. Each entry is appended to the parent as a separate proposed program, so four proposals give four alternative programs, not one program with four new operations. These programs are executed, measured, and submitted for visual acceptance. A repeated request continues the same list, and when the list is exhausted, the tool disappears from that candidate’s row. The tool matters most on parts where every first operation sampled from the generator gives an open surface rather than a solid. The search cannot continue from such a result, while an extrusion of a cross-section of the target gives a closed solid to build on (Section 4.6). Parameter optimization. The optimizer changes the numbers in an existing candidate program but keeps its operations. The free parameters are the sketch coordinates and radii and the extrusion depths; the sketch planes and the revolve axes and angles stay fixed. To compare the program with the target, the optimizer uses signed distances: for a point in space, the distance to the surface of a solid, negative inside it. The distance to the program’s solid is computed directly from its operations, and the distance to the target is computed from the mesh at sampled points. The mismatch between the program and the target is the mean squared difference of the two distances over these points. Its gradient is estimated numerically: each parameter in turn is shifted by a small step, and the change in the mismatch gives the derivative with respect to that parameter. The optimizer then updates all parameters and repeats the step. It first fits points spread over the whole part, then points close to the target surface. Of the starting, coarse, and fine parameters, it keeps those that match best near the surface, so the program may also come back unchanged. The refined program is executed and measured, and becomes a new child of the selected candidate with the same operations if visually accepted. The optimizer handles extrusions, holes, and revolves; programs with other operations cannot be refined. It fits distances, not the IoU/GMS score, so whether the child is better is decided by the score (Eq. 2). The tool is deterministic and is therefore offered once per candidate. 3.5 Execution, Measurements, and Protected Best A tool response is only a proposal. After technical validation and measurement, the assistant inspects its rendered geometry and decides whether to accept it into the candidate pool. Only accepted proposals become candidates. Execution runs separately from the assistant. A candidate is invalid if its program does not build or its mesh is not, as a whole, a watertight solid with positive volume. This is stricter than the evaluation code of CADENA [Kabisov et al., 2026b], which accepts a prediction if any connected component is a closed solid and computes IoU on that component. A candidate whose execution or measurement exceeds the time limit also counts as invalid. The execution component records which of these happened. Whether a candidate is valid and how close it is to the target are reported separately. Before measuring, the target and the candidate are placed in a common frame. The target is centered by its bounding box and scaled uniformly by its largest dimension. The candidate is brought to the same scale by one fixed transform of the modeling coordinates, shared by all candidates, rather than by fitting its own bounding box. A candidate of the wrong size therefore scores lower instead of having its scale error normalized away. Two metrics compare a candidate with the target. Intersection-over-Union (IoU) measures volumetric overlap: I i = V (M ⋆ ∩E (p i )) V (M ⋆ ∪E (p i )) .(1) The Generalized Match Score (GMS) measures how well the two surfaces and their normals agree. We use the definition of Kabisov et al. [2026b], whose raw value is an area over a curve on the angle range[0 ◦ , 25 ◦ ]and therefore lies in [0, 25], and normalize it asH i = 1− GMS raw,i /25, so that both metrics lie in[0, 1]and higher is better. IoU requires a target that is a single watertight solid with nonzero volume; for any other target only GMS is available. 6 CADFatherA PREPRINT Figure 3: A reconstruction trajectory on an MCB part (a chain link). The figure follows the lineage of the final result, one column per assistant step or group of steps: above each render are the tools called in those steps, with the tool that produced the shown candidate in bold; below it are the candidate ID, IoU, and GMS. The algorithmic start c5 recovers one post, a warm algorithmic proposal adds the lower plate (c13), and learned operation proposals add the second post (c15) and the upper plate (c20); in the same steps the first operations proposed by the learned tool produce only open shells, and the other children score lower. In steps 5–6 the gains become small; the candidate c26 from step 7 has a higher IoU but a lower GMS than c25, and in step 8 the assistant ends the part withfinish(stalled), and the output is the protected best c25. The score of a candidate is the mean of the metrics available for it: s i = 1 |Q i | X q∈Q i q, Q i ⊆I i , H i ,(2) that is, the average of IoU and GMS, or GMS alone for a target without IoU. An invalid candidate scores s i = 0. The agent maintains a protected best result using Eq. 2. This result is retained even if the assistant continues another branch. A valid candidate always takes precedence over an invalid one. The final output is this protected best, not the last candidate the assistant worked on. The assistant may judge progress in its own terms when choosing tools, while Eq. 2 determines the score used to select the final result. Since the target mesh is the input of the task, this selection uses no information beyond the input; it is, however, a best-of-N choice by the same metrics that are reported in Section 4. 3.6 Budgets, Recovery, and Termination Each part has a limited budget for every tool. The candidate table shows what is still available: a tool disappears from a row once its budget is spent, and the sample limit shrinks as generator samples are used. A request that exceeds the budget is reduced or rejected, and the assistant is told why. Afinishcall ends the reconstruction of the whole part, not of a single branch. The assistant gives one of two reasons: shape, when the assistant judges that the best candidate reproduces every feature of the target and only small numerical differences remain, orstalled, when some feature is still wrong but recent steps no longer improve the result and no other action seems worth trying. The prompt presentsstalledas a normal outcome, not a failure. Afinishcall is ignored until at least one valid candidate exists. Independently of the assistant, fixed limits on the number of steps and on running time guarantee that every part terminates. A malformed reply from the assistant does not end the part. If the reply calls no tool or requests only actions that are not available, the agent requests a revised action, stating the reason and the available actions. If this also fails, the agent performs the cheapest available action on the best candidate and tells the assistant about it. Failed executions are likewise reported back to the assistant, and the protected best is never lost. Figure 3 follows one reconstruction from the first step to the finish call. 4 Experiments 4.1 Datasets and Setup We use the full test sets of DeepCAD, Fusion360, and MCB, containing 8046, 1725, and 5000 parts, respectively [Wu et al., 2021, Willis et al., 2021, Kim et al., 2020]. Ablations use fixed 1000-part subsets of each test set. In addition, 7 CADFatherA PREPRINT Table 1: Comparison on the full test sets. All rows except CADFather are published results [Kabisov et al., 2026b]: the baselines (CAD-Recode [Rukhovich et al., 2025], cadrille [Kolodiazhnyi et al., 2025], CADReasoner [Kabisov et al., 2026a], CADEvolve [Elistratov et al., 2026], CADFit [Nehme et al., 2026]), CADENA-SFT and CADENA-RL greedy from its external-dataset table, CADENA-RL sampling from its decoding-strategy table (T = 1, 12 samples per operation). Published CADENA rows use CADENA’s own validity rule, which is more lenient than ours (Section 3.5); their IR is not directly comparable to the IR of CADFather. All means are taken over valid predictions only, so a high IR leaves the means computed over an easier subset. † CADFit is an optimization loop run under a fixed compute budget; unconverged parts are counted in IR, and its prediction and target are normalized alike. IoU and GMS are means, CD values are medians scaled by 10 3 , and IR is a fraction. DatasetMethodIRIoUGMSCD 8k CD 30k DeepCADCAD-Recode0.07900.9140.9290.170.055 cadrille0.00300.8970.9480.170.059 CADReasoner0.03000.9100.9490.160.049 CADEvolve0.00900.9240.9530.160.050 CADFit † 0.27500.9140.8980.180.052 CADENA-SFT greedy0.02600.9170.9530.160.048 CADENA-RL greedy0.00300.9610.9700.15 0.042 CADENA-RL sampling0.00070.9660.9740.150.042 CADFather0.00000.9870.9830.1380.039 Fusion360CAD-Recode0.13600.8720.8580.170.060 cadrille0.00800.8480.8680.170.066 CADReasoner0.07200.8630.8860.150.050 CADEvolve0.02700.8810.8820.160.056 CADFit † 0.25600.8820.8460.170.054 CADENA-SFT greedy0.03800.8880.9080.140.046 CADENA-RL greedy0.01200.9410.9330.12 0.038 CADENA-RL sampling0.00230.9520.9420.120.036 CADFather0.00000.9760.9600.1150.034 MCBCAD-Recode0.21500.7110.5470.660.524 cadrille0.01500.6620.5500.850.720 CADReasoner0.31700.6900.5521.441.290 CADEvolve0.09200.7290.5830.630.500 CADFit † 0.29700.7580.6010.480.365 CADENA-SFT greedy0.12000.7520.6340.430.259 CADENA-RL greedy0.00700.8820.7370.22 0.093 CADENA-RL sampling0.0006 0.8950.7510.220.089 CADFather0.00000.9130.7660.2100.083 we evaluate once on CADENA-Bench [Kabisov et al., 2026b], a benchmark of 3396 mechanical parts in six families drawn from TMCAD [Zou and Zhu, 2025], MCB [Kim et al., 2020], and CADNET [Manda et al., 2021]. We also evaluate once, with the same configuration, on two recent benchmarks: CADBench [Doris et al., 2026], 18000 parts in six families of 3000 (Base, Fusion, Extrude, and All-Ops from STEP models, Mechanical and Organic from meshes), using its clean target meshes; and BenchCAD [Zhang et al., 2026], 17900 CadQuery programs from 106 industrial part families in three difficulty tiers. The CADENA-RL checkpoint used for learned operation proposals (Section 3) is served in bfloat16. The assistant is Qwen3.8-27B with FP8 weights; explicit thinking is disabled. Both models are frozen. Per part, the limits are 24 assistant steps, at most 12 operations in a program, and 1000 seconds of wall time; the budgets are 80 generator samples, 6 algorithmic-proposal calls, 10 optimizer calls, and 120 program executions. A single learned call requests at most 32 samples. Building and measuring one candidate is limited to 30 seconds. The tool set is the one described in Section 3.4. 4.2 Metrics and Comparison Protocol Besides IoU and GMS (Section 3.5), Chamfer distance (CD) measures distances between sampled surfaces. We report the invalidity ratio (IR), mean IoU, mean GMS, and median CD at 8192 and 30000 sampled points, with CD multiplied by10 3 . Validity, the common frame, and the GMS normalization are those of Section 3.5; the frame and the GMS normalization coincide with the protocol of CADENA [Kabisov et al., 2026b], while our validity rule is stricter than 8 CADFatherA PREPRINT Table 2: CADFather on CADENA-Bench by part family, and over all parts against published results.nis the number of parts; IoU and GMS are means, CD values are medians over all parts scaled by10 3 . The tooling-and-gauges family has 17 parts and is shown for completeness only. Published rows come from the full-benchmark table of Kabisov et al. [2026b]; there CD, IoU, and GMS are computed over valid predictions only, so each row describes a different subset whose size is given by IR. † As in Table 1. FamilynIRIoUGMSCD 8k CD 30k Shafts and bushings7620.00000.9430.7640.2690.093 Gears and bearings7490.00000.8800.6600.4230.241 Housings and frames3590.00000.9170.7720.3850.245 Levers and profiles4630.00000.9340.8190.1390.048 Springs and fasteners10460.00000.8900.6720.3200.173 Tooling and gauges170.00000.9280.6280.3510.158 All33960.00000.9090.7210.2930.136 All parts, published results [Kabisov et al., 2026b] CAD-Recode33960.27900.6860.4891.0610.905 cadrille33960.0080 0.6880.4981.2671.125 CADReasoner33960.39900.6830.5291.9711.833 CADEvolve33960.10800.7300.5291.3121.143 CADFit † 33960.18800.7570.5480.7130.536 CADENA-SFT greedy33960.12800.7390.5800.9640.774 CADENA-RL greedy33960.01600.8760.6700.3310.176 CADENA’s. IoU is computed only for targets whose mesh is a single watertight solid with nonzero volume; GMS and CD cover all targets, including open ones. Unless stated otherwise, IoU, GMS, and CD are taken over valid predictions, as in CADENA. Published CADENA results are taken from the original paper. 4.3 Main Results Table 1 compares CADFather with the published CADENA results and the baselines evaluated in that paper. On DeepCAD, CADFather reaches a mean IoU of 0.987 against 0.966 for CADENA-RL with sampling; on Fusion360, 0.976 against 0.952; on MCB, 0.913 against 0.895. The invalidity ratio is zero on all three datasets: every part ends with a closed solid. The IoU gain over sampling is of similar size on all three datasets (0.018–0.024), and mean GMS is higher as well (0.983, 0.960, and 0.766 against 0.974, 0.942, and 0.751). Median CD is lower on all three datasets at both sampling densities (at 30000 points, 0.039, 0.034, and 0.083 against 0.042, 0.036, and 0.089). The learned tool uses the same CADENA-RL checkpoint, so the gain does not come from a stronger generator. The ablations (Section 4.6) compare configurations of CADFather with each other rather than with CADENA; among them, removing algorithmic proposals costs the most: it lowers the mean score by 0.012–0.110 on the 1000-part subsets and raises IR from zero to 0.007–0.124, whereas removing the optimizer lowers the mean score by only 0.004–0.006 and leaves IR at zero. Mean GMS on MCB remains 0.766, well below the IoU; the two means cover different subsets of targets, but the gap suggests that matching volume does not imply matching surface structure on mechanical components. Across DeepCAD, Fusion360, and MCB, CADFather achieves the best reported IR, mean IoU, mean GMS, and median CD at both sampling densities among all methods compared in Table 1. 4.4 Evaluation on CADENA-Bench Table 2 reports CADFather on CADENA-Bench with the configuration of the main runs. The invalidity ratio is again zero, and the mean IoU of 0.909 over the 2240 targets with defined IoU is close to that on MCB (0.913). As on MCB, where 58% of the targets have a defined IoU, only 66% do here, against 95–99% on DeepCAD and Fusion360, so on mechanical parts GMS, which covers all targets, carries a larger part of the comparison. The shaft-and-bushing and lever-and-profile families are reconstructed best; among families with enough parts to compare, the gear-and-bearing and spring-and-fastener families have the lowest IoU and GMS. Over all parts, the mean IoU of 0.909 and GMS of 0.721 compare with 0.876 and 0.670 for CADENA-RL greedy, the strongest published row; CADENA does not report its sampling variant on this benchmark. The three sources reach the same mean IoU (0.909–0.910 for CADNET, MCB, and TMCAD). 9 CADFatherA PREPRINT Table 3: CADFather on CADBench and BenchCAD over all parts, under our protocol (Section 4.2). IoU and GMS are means, CD values are medians scaled by 10 3 . BenchmarkIRIoU GMS CD 8k CD 30k CADBench 0.0007 0.904 0.815 0.1450.048 BenchCAD 0.0000 0.948 0.873 0.1600.050 Table 4: Mesh-to-CAD results on CADBench with its evalua- tion code, aggregated over all 18000 parts. Rows other than CADFather are published results of Doris et al. [2026] (clean meshes; mean of three runs for non-deterministic methods). CADFather is a single run; its programs use our operation library on top of CadQuery, so program-length metrics (token and operation counts) are not comparable and are omitted. CD is scaled as in Doris et al. [2026]. MethodIoU↑SIoU↑CD↓VSR↑ CAD-Recode0.6730.5030.0560.912 CADEvolve0.7070.4980.0620.967 cadrille0.6870.5170.0560.939 CADFit0.859 0.6790.0380.981 CADFather0.9300.7870.0290.968 Table 5: Vision2Code voxel IoU and invalid rate on BenchCAD. Image-conditioned methods receive four orthographic views; with tools, the model also gets a Python sandbox to render, measure, and iterate before submitting. Frontier models are taken from the BenchCAD leaderboard [BenchCAD Team, 2026]; ∗ self-reported by the vendor, without IR. CADENA-RL is reported by Kabisov et al. [2026b], the other open methods by Zhang et al. [2026]. Parts: the number of the 17 900 BenchCAD parts a row is evaluated on; 1000 is a random subset drawn by the vendor (for Claude, a mean over five runs) and by us for CADFather; n/s, not stated. Other rows are published by Zhang et al. [2026] and Kabisov et al. [2026b]. MethodInputPartsVoxel IoU↑IR (%)↓ Claude Sonnet 5.5 (max) ∗ image10000.747– Claude Opus 5.5 (max) ∗ image10000.730– GPT-5.6 Sol (max) ∗ imagen/s0.706– Gemini 3.1 Pro (thinking)imagen/s0.35518.5 Claude Opus 4.7 (thinking)imagen/s0.2793.5 Claude Sonnet 5.5 (max) ∗ image + tools10000.963– Claude Opus 5.5 (max) ∗ image + tools10000.962– GPT-6 Astra ∗ image + tools10000.959– GPT-5.6 Sol (max) ∗ image + toolsn/s0.834– cadrille-RLimagen/s0.0688.8 CADEvolve v3imagen/s0.7507.3 Qwen3-VL-2B RL, in-distribution [Zhang et al., 2026]imagen/s0.7521.1 CADENA-RLmesh17 9000.9100.9 CADFathermesh10000.9680.0 4.5 CADBench and BenchCAD Table 3 reports CADFather on CADBench and BenchCAD under our protocol. On CADBench, 12 of the 18000 parts end without a valid prediction (IR 0.0007). On all of them the target mesh is so dense that computing the IoU of an overlapping candidate exceeds the 30 s execution limit, so every candidate fails. The mean IoU over the 17314 targets with defined IoU is 0.904. Quality follows the families: the Base family of sketch-and-extrude parts is reconstructed almost exactly (IoU 0.980, GMS 0.974), while the Organic family of object-like meshes is the hardest (IoU 0.759, GMS 0.548). On BenchCAD, every prediction is valid, the mean IoU is 0.948 over 16350 targets, and IoU and GMS decrease monotonically from the easy to the hard tier (0.956 to 0.938 and 0.886 to 0.859). The lowest scores fall on helical springs and twist drills, which remain poor even on targets with defined IoU. For comparison with published methods, Table 4 evaluates the final programs of all 18000 CADBench parts with the benchmark’s own evaluation code and aggregation [Doris et al., 2026]: aligned IoU and surface IoU (SIoU) are medians with failures counted as zero, CD is the median over successfully evaluated programs, and the valid shape rate (VSR) is the fraction of programs that produce a valid shape; each metric is aggregated over the 14 complexity splits weighted by their size. CADFather reaches higher IoU and SIoU and lower CD than all published mesh-to-CAD methods, including CADFit, and is better than CADFit on each of the 14 splits in these three metrics. Its VSR is lower than that of CADFit: 576 parts exceed the evaluator’s 30 s limit, which covers program execution and all metric computations for a part. 10 CADFatherA PREPRINT $0.01$0.1$1$10 API cost per part (USD, log scale) 30% 40% 50% 60% 70% 80% 90% 100% Mean voxel IoU CADFather GPT-6 Astra GPT-5.6 Sol Claude Opus 5.5 Figure 4: Voxel IoU on BenchCAD against estimated token cost per part (log scale). CADFather is evaluated on 1000 parts drawn at random; each point is the mean after the firstkassistant steps of one full-budget run (k = 1, 2, 3, 4, 6, 8, 12, 24), and the dashed line marks its full-budget level. Assistant and generator tokens are both priced at the OpenRouter rate for Qwen3.8-27B ($0.425 and $2.55 per million input and output tokens). Frontier curves are taken from the BenchCAD leaderboard [BenchCAD Team, 2026]. Published BenchCAD results follow its Vision2Code protocol: voxel IoU on a64 3 grid and the invalid rate (IR), i.e., the fraction of generated programs that fail to execute [Zhang et al., 2026]. Table 5 places CADFather beside the published entries; we score it with the voxelization from the BenchCAD evaluation code. CADFather reaches a voxel IoU of 0.968 with no invalid predictions, against 0.910 for CADENA-RL, the other mesh-conditioned entry, and at most 0.752 for image-conditioned systems without tools. Frontier models with a Python sandbox self-report up to 0.963 on 1 000-part subsets. Figure 4 relates voxel IoU to estimated token cost per part. For CADFather, this estimate covers model tokens and excludes geometric processing and execution. CADFather reaches an IoU of 0.943 after four assistant steps at $0.016 per part, and 0.968 at its full budget of $0.046 per part. For comparison, Claude Opus 5.5 and GPT-6 Astra with tools report 0.962 at $5.94 per part and 0.959 at $1.75 per part, respectively. These published entries use different inputs and evaluated subsets, so the comparison is contextual. 4.6 Ablations The ablations assess the effects of removing algorithmic proposals, parameter optimization, or both under identical configured budgets, limits, and model servers. They do not match consumed compute or isolate the contribution of the assistant’s selection policy. •Learned only: algorithmic proposals and optimization are removed; the generator-sample budget is unchanged, so the arm tests whether tool diversity adds value beyond sampling at a matched generation budget. This arm is not CADENA sampling: CADFather never extends an invalid candidate, so a part whose first operations all produce non-watertight meshes ends invalid, whereas CADENA’s sampling continues from any candidate that receives a reward. • w/o algorithmic proposals: both entry points of the algorithmic tool are removed. • w/o optimization: the parameter optimizer is removed. Differences are reported against the full-tool control on the same subset as paired per-part differences in the score of Eq. 2, with 95% bootstrap confidence intervals over parts (2000 resamples). Unlike the IoU and GMS means, the score difference covers all parts, with an invalid prediction scored as zero. 11 CADFatherA PREPRINT Table 6: Ablations on 1000-part subsets.∆sis the paired difference in mean score (Eq. 2) to the full-tool control with a 95% bootstrap interval, taken over all 1000 parts with invalid predictions scored as zero; IR is a fraction. IoU and GMS are means over valid predictions; IoU covers only the 565 (MCB), 983 (DeepCAD), and 949 (Fusion360) targets with defined IoU. DatasetConfigurationIRIoU GMS∆s [95% CI] MCBFull (control)0.000 0.904 0.756— Learned only0.1230.872 0.735 −0.1135 [−0.1303,−0.0979] w/o algorithmic proposals 0.124 0.882 0.739 −0.1095 [−0.1265,−0.0942] w/o optimization0.000 0.8950.750−0.0061 [−0.0088,−0.0034] DeepCAD Full (control)0.000 0.984 0.983— Learned only0.0070.960 0.979−0.0201 [−0.0254,−0.0152] w/o algorithmic proposals 0.0070.9760.979−0.0124[−0.0176,−0.0076] w/o optimization0.000 0.975 0.983 −0.0045 [−0.0059,−0.0030] Fusion360 Full (control)0.000 0.976 0.958— Learned only0.0120.952 0.951 −0.0266 [−0.0335,−0.0200] w/o algorithmic proposals 0.0120.966 0.952−0.0192[−0.0260,−0.0129] w/o optimization0.000 0.9680.958 −0.0042 [−0.0062,−0.0023] Table 7: Per-part cost of CADFather on the full test sets and CADENA-Bench (means). Tool calls count requests; generator samples count proposals across learned requests. A part is finished by the assistant when it ends with a finish call while an affordable action remains. DeepCADFusion360MCBCADENA-Bench Assistant steps6.378.4112.2513.04 Tool calls8.6712.4320.5723.01 learned / algorithmic / optimization4.57 / 1.81 / 2.296.60 / 2.72 / 3.1010.96 / 4.94 / 4.6812.38 / 5.34 / 5.29 Generator samples19.031.961.167.1 Calls yielding an executable candidate (%)83.385.989.890.0 Calls raising the protected best (%)29.029.630.036.1 Parts finished by the assistant (%)86.173.437.325.0 Wall time per part (s)82.6119.9245.6306.7 Removing algorithmic proposals and parameter optimization changes the mean score by−0.114on MCB, about as much as removing algorithmic proposals alone (−0.110) and far more than removing optimization alone (−0.006). Algorithmic proposals carry most of the gain: without them the invalidity ratio on MCB rises from zero to 0.12. Nearly all of these failures are non-watertight results of parts on which no sampled first operation yields a closed solid, so the search cannot proceed from a valid base; algorithmic proposals supply such a base. Since an invalid prediction scores zero, this rise alone accounts for most of the−0.11on MCB, while the IoU and GMS of the remaining valid predictions drop by only 0.02–0.03. On MCB, the optimizer adds almost nothing on top of learned proposal generation, and w/o algorithmic proposals and learned only are close. On DeepCAD and Fusion360 the ordering of the arms is the same at a smaller scale, but there the optimizer on top of learned proposal generation adds about 0.008, more than its own contribution in the full configuration. Candidate-level best updates, not tool invocation counts, indicate whether a tool supplied a useful result: on the three full test sets, 27–36% of learned calls, 25–29% of algorithmic-proposal calls, and 18–34% of optimizer calls raised the protected best. These shares favor tools that are called early in a part, when the best is still easy to raise. Figure 5 shows parts on which the full configuration scores above all three ablations: in these examples, the arms without algorithmic proposals lose a whole feature, produce a non-watertight body, or fail to execute. 4.7 Efficiency and Qualitative Analysis Table 7 reports the per-part cost of the full configuration. Wall time depends on hardware, model serving, and concurrency; it is reported for the stated deployment and does not by itself establish an algorithmic speedup. The assistant ends 86.1%, 73.4%, and 37.3% of parts itself on DeepCAD, Fusion360, and MCB, and 90.2%, 82.3%, and 50.9% of these endings give the reasonshape; the remaining parts stop when no affordable action is left or at the step, execution, or wall-time limits. Mechanical parts take about twice as many assistant steps as DeepCAD parts (12.3 on MCB against 6.4 on DeepCAD and 8.4 on Fusion360) and about three times the wall time. CADENA-Bench is the 12 CADFatherA PREPRINT Figure 5: Examples from the ablation subsets. Each row is one part: the target (GT) and the final results of the full configuration, learned only, w/o algorithmic proposals (w/o det), and w/o optimization, rendered in a common frame. Above each result are its score (Eq. 2; zero for an invalid prediction) and the number of tool calls on the lineage of that result (det counts both algorithmic entry points). Figure 6: Comparison with CADENA, CADFit, and two frontier coding agents. Each row is one part: the target, CADFather (Ours), CADENA-RL, CADFit † , and the reconstructions of Claude Opus 5.5 and GPT-6 Astra. The frontier agents wrote CadQuery code with access to the target mesh and received the score against the target after every attempt. most expensive set: 13.0 steps and 307 s per part, with only 25.0% of parts ended by the assistant (55.2% of them with shape). Figure 3 shows a trace whose decisions and measurements were verified against the logs. 13 CADFatherA PREPRINT Figure 6 shows parts on which CADFather is well ahead of CADENA and CADFit. These methods miss whole features, such as the pins of a chain link or the teeth of a gear, or build a different overall layout, while CADFather recovers the structure of the part. Two frontier coding agents, Claude Opus 5.5 and GPT-6 Astra, given the target mesh and the score after every attempt, reach scores close to those of CADFather on these parts. Typical failure cases are an incorrect initial topology that later operations cannot recover, an attractive overlap score with poor surface agreement, and a part terminated by a resource limit. In the first case, the branches that survive all descend from one wrong root: a solid block is rebuilt as a hollow frame, or a ladder’s rungs merge into one plate. In the second case (Figure 7, left), the volume is matched while fine surface structure such as a knurl or shallow pockets is never built; on the panel, the assistant judged the remaining gap numerical and stopped. A resource limit can stop a part that was still improving, as on the bracket, or exhaust the wall time on a complex geometry before a correct base exists, as on the helical spring rebuilt as a tube (Figure 7, right). Figure 7: Failure cases from the full test sets. Each pair shows the target and the CADFather result in a common frame, with IoU and GMS above the result. Left: high IoU with low GMS, where the volume is matched but the knurl (MCB) and the shallow pockets (Fusion360) are missing. Right: parts stopped by the wall-time limit (MCB, a spring reconstructed as a tube) and by the execution limit (Fusion360, a bracket with incomplete ribs). 5 Limitations CADFather remains limited by the operations supported by its CAD representation and the proposals its tools can produce. Parameter optimization can refine an existing program but cannot correct an unsuitable sequence of operations; likewise, retaining earlier candidates does not help if a useful alternative was never generated. Search limits may also terminate a trajectory that would have succeeded with more computation. The assistant decides which candidates and tools to use from incomplete visual and numerical evidence. Its decisions can depend on the prompt, model behavior, and which candidates are available for inspection. This flexibility therefore does not guarantee that the best reconstruction will be found. Our evaluation measures geometric reconstruction and program validity, not recovery of the original design history, manufacturing intent, or engineering constraints. It covers individual parts rather than assemblies, tolerances, or simulation-validated designs. CADFather also incurs computational costs for planning, inspection, and executing alternatives. The ablations use fixed budgets but are limited to 1,000-part subsets; adapting agent baselines such as CAD-Assistant and IterCAD for a direct comparison remains future work. 14 CADFatherA PREPRINT 6 Conclusion We presented CADFather, an autonomous agent for reconstructing executable CAD programs from target meshes. A vision-language assistant inspects the target and intermediate reconstructions, selects candidate programs and tools, and uses execution feedback to guide subsequent decisions. Learned and algorithmic proposals provide alternative modeling operations, while parameter optimization refines existing programs. The system preserves the best valid candidate as it explores alternative reconstructions, without additional training of either model. Across the full DeepCAD, Fusion360, and MCB test sets, CADFather improves mean IoU and GMS and reduces median Chamfer distance relative to the published CADENA-RL sampling results. It produces valid outputs for every part in these tests under its stricter validity rule. CADFather also improves on the published CADENA-RL greedy results on CADENA-Bench. On CADBench, it achieves higher IoU and surface IoU and lower Chamfer distance than the reported mesh-to-CAD baselines, although its valid shape rate is below that of CADFit. On BenchCAD, CADFather achieves higher voxel IoU than the frontier models in our comparison, at up to100×lower estimated inference cost. Overall, the results support coordinating complementary reconstruction tools rather than committing to a single source of CAD operations. Direct comparisons with other CAD agents and a controlled evaluation of the assistant’s tool-selection policy remain future work. References Danila Rukhovich, Elona Dupont, Dimitrios Mallis, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. CAD- Recode: Reverse engineering CAD code from point clouds. In IEEE/CVF International Conference on Computer Vision (ICCV), 2025. Maksim Kolodiazhnyi, Denis Tarasov, Dmitrii Zhemchuzhnikov, Alexander Nikulin, Ilya Zisman, Anna Vorontsova, Anton Konushin, Vladislav Kurenkov, and Danila Rukhovich. cadrille: Multi-modal CAD reconstruction with reinforcement learning. arXiv preprint arXiv:2505.22914, 2025. Maksim Elistratov, Marina Barannikov, Gregory Ivanov, Valentin Khrulkov, Anton Konushin, Andrey Kuznetsov, and Dmitrii Zhemchuzhnikov. 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