AnchorGen: Anchored Optimization for Customizable Generative 3D Design

Hantao Zhang; Oliver Heinimann; Jieke Wu; Yingxuan You; Emilien Seiler; Pascal Fua

cs.CVOct 5, 2026

AnchorGen: Anchored Optimization for Customizable Generative 3D Design

Authors: Hantao Zhang, Oliver Heinimann, Jieke Wu, Yingxuan You, Emilien Seiler, Pascal Fua

Organizations: CVLab, EPFL, Switzerland

Abstract

Engineering design often starts from a 2D sketch that fixes style and proportions, yet the subsequent 3D shape optimization relies on learned generative priors to keep the geometry valid. However, these priors are agnostic to the sketch: while they admit a valid design by correcting a drifted proposal back to its training distribution, they often correct it towards the high-density region, ignoring the specified design. We introduce \emph{AnchorGen}, a rectified-flow framework trained unconditionally on the concatenated shape and sketch latents of paired data. The learned manifold represents the joint distribution of shape-sketch pairs, so constraining the sketch component restricts the iterate to the sub-manifold of shapes consistent with a target style. Since training employs no conditioning signal, the constraint is imposed at inference: gradient descent optimizes the shape latent to minimize a differentiable drag surrogate, while constraining the sketch latent to remain close to the target sketch via a token-wise cosine penalty. A single model thereby supports design-preserving optimization, dimensionally explicit design edits, and sketch-only synthesis.

Figures & tables

Figure 1: Sketch-anchored shape optimization. AnchorGen reduces the aerodynamic drag of a 3D vehicle while anchoring the optimization to a 2D sketch that encodes the design intent. (a) Preserving a design. Reducing the drag by $10\%$ without a sketch anchor, as in FCSO ( Seiler et al., 2026 ) , changes the vehicle’s identity: the front end is restyled (green) and an unintended rear wing appears (red). With the sketch of the initial shape as an anchor, AnchorGen reaches the same drag reduction and preserves both regions. (b) Modifying a design. Adding a spoiler to the sketch (red) produces an optimized shape with a more aerodynamic spoiler, while leaving the rest unchanged.

Figure 2: Framework. (a) Two encoders, one for shape and one for sketches, are trained separately. (b) Given the encoders and their latent vectors, a flow matching algorithm is trained to produce them jointly from a single normal distribution. (c) At inference, a joint latent vector is generated, re-noised, and optimized to minimize the target physical objective while remaining close to the latent vector corresponding to the target sketch.

Method	FD ${}_{\text{incep}}$ $\downarrow$	KD ${}_{\text{incep}}$ $\downarrow$	FD ${}_{\text{dino}}$ $\downarrow$	KD ${}_{\text{dino}}$ $\downarrow$	FD ${}_{\text{point}}$ $\downarrow$	KD ${}_{\text{point}}$ $\downarrow$
GD ( 2025 )	132.82	106.26	97.97	75.63	37.50	123.20
FMG ( 2022 )	100.20	67.02	77.05	56.52	25.00	73.00
D-Flow ( 2024 )	108.79	76.44	82.85	62.68	29.95	76.70
ICTM ( 2024 )	101.73	75.52	75.71	58.31	24.97	77.60
SGO ( 2026 )	107.72	76.89	81.54	61.25	30.75	83.70
FCSO ( 2026 )	89.08	55.91	69.20	52.72	20.96	51.40

Table 1: Distributional Similarity. Car drag optimization at

30\%

drag reduction. Metrics are scaled:

\text{KD}_{\text{incep}}

(

\times 10^{3}

\text{FD}_{\text{dino}}

(

\times 10^{-1}

\text{FD}_{\text{point}}

(

\times 10^{2}

), and

\text{KD}_{\text{point}}

(

\times 10^{5}

Figure 3: Preservation of shape identity at a $10\%$ drag reduction. Green boxes mark identity features of the initial shape.

Method	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio $\uparrow$	Normal-C $\uparrow$	HD95 $\downarrow$	Avg. Dim-Err $\downarrow$
GD ( 2025 )	73.30	47.22	1.672	91.88	89.44	2.576	4.69
FMG † ( 2022 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
D-Flow ( 2024 )	65.91	44.64	1.923	88.06	87.81	2.821	4.18
ICTM † ( 2024 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
SGO † ( 2026 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
FCSO ( 2026 )	73.44	48.24	1.661	92.04	89.44	2.587	4.37

Table 2: Pairwise similarity for dimension edits on DrivAerNet++. Similarity to the target shape over

600

source–target pairs at a

20\%

drag reduction, averaged over the three views. Top: prior-based methods, which steer a shape-only prior at test time. Middle: conditioning-based methods, which train a sketch-conditioned prior and inject the sketch via input conditioning or classifier-free guidance. Bottom: AnchorGen , which trains a single prior over shape-sketch pairs. Metrics are scaled by

\times 100

; NaN marks an optimization that became unstable and collapsed.

Figure 4: Customized Design under a Drag Objective. Starting from a base vehicle shape with a user-added rear spoiler, we show how the shape evolves under the drag optimization objective while the specified modification is preserved.

Figure 5: Generation from scratch. Generation starts from noise, with the shape and decoded sketch shown over $60$ sketch-anchored optimization iterations. (a) Training-style sketches. (b) Simple line drawings in a zero-shot setting.

Method	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio ∗	Normal-C $\uparrow$	HD95 $\downarrow$	L-Err $\downarrow$	Drag (CFD) $\downarrow$
PhysGen ( 2026 )	64.66	42.56	1.85	104.12	89.55	2.46	3.21	0.2505
AnchorGen (Ours)	63.50	40.31	1.98	89.26	85.61	2.54	2.43	0.1894

Table 3: Generation from scratch, anchored to a given target sketch.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Sketch/Drag weight ratio ablation. F@ $0.5\%$ ( $\times 100$ , $\uparrow$ ) versus the Sketch/Drag weight ratio, over the $20$ source cases. (a) With an exogenous target sketch, measured between the optimized output and the target shape. (b) With the anchor’s own sketch, measured between the output and its source shape. Dashed lines denote the FCSO baseline.

Figure 7: Visualization of the Shape over 100 Optimization Iterations for Customized Design.

Figure 8: Controlled-dimension error over aerodynamic optimization.

Figure 9: Target-shape similarity over aerodynamic optimization.

Method	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio $\uparrow$	Normal-C $\uparrow$	HD95 $\downarrow$	W-Err $\downarrow$
GD ( 2025 )	64.98	44.88	1.93	92.80	87.62	2.55	1.35
FMG † ( 2022 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
D-Flow ( 2024 )	67.06	48.83	2.00	88.89	87.46	2.76	1.03
ICTM † ( 2024 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
SGO † ( 2026 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
FCSO ( 2026 )	64.66	44.36	1.94	92.96	87.42	2.57	1.23

Appendix

Table 4: Evaluation at the

20\%

target drag reduction for the Front View (Width) setting (

n=200

). All metrics are scaled by

\times 100

Method	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio $\uparrow$	Normal-C $\uparrow$	HD95 $\downarrow$	H-Err $\downarrow$
GD ( 2025 )	77.50	47.17	1.48	91.43	91.57	2.23	7.88
FMG † ( 2022 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
D-Flow ( 2024 )	64.83	41.82	1.83	87.65	88.80	2.51	6.74
ICTM † ( 2024 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
SGO † ( 2026 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
FCSO ( 2026 )	77.68	48.82	1.46	91.59	91.53	2.24	7.03

Appendix

Table 5: Evaluation at the

20\%

target drag reduction for the Rear View (Height) setting (

n=200

). All metrics are scaled by

\times 100

Method	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio $\uparrow$	Normal-C $\uparrow$	HD95 $\downarrow$	L-Err $\downarrow$
GD ( 2025 )	77.42	49.60	1.61	91.42	89.14	2.95	4.83
FMG † ( 2022 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
D-Flow ( 2024 )	65.83	43.29	1.94	87.65	87.16	3.20	4.76
ICTM † ( 2024 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
SGO † ( 2026 )	NaN	NaN	NaN	NaN	NaN	NaN	NaN
FCSO ( 2026 )	77.97	51.54	1.58	91.58	89.38	2.96	4.85

Appendix

Table 6: Evaluation at the

20\%

target drag reduction for the Side View (Length) setting (

n=200

). All metrics are scaled by

\times 100

Figure 10: Front view (width). Effect of the target sketch anchor. The width of the shape corresponding to the target sketch is taken as $1$ , and we report the ratio to that width reached after a $20\%$ drag reduction.

Figure 11: Rear view (height). Effect of the target sketch anchor. The height of the shape corresponding to the target sketch is taken as $1$ , and we report the ratio to that height reached after a $20\%$ drag reduction.

Figure 12: Side view (length). Effect of the target sketch anchor. The length of the shape corresponding to the target sketch is taken as $1$ , and we report the ratio to that length reached after a $20\%$ drag reduction.

$\bm{\tau}$	F@1% $\uparrow$	F@0.5% $\uparrow$	CD-L1 $\downarrow$	Vol-Ratio $\uparrow$	Normal-C $\uparrow$	HD95 $\downarrow$	W-Err $\downarrow$
$0.1$	66.51	45.22	1.85	93.59	88.23	2.45	1.23
$0.2$	72.14	48.62	1.64	94.53	89.62	2.33	0.81
$0.3$	76.78	52.56	1.50	94.70	90.69	2.30	0.62
$0.4$	80.26	57.02	1.41	94.75	91.31	2.35	0.58
$0.5$	82.30	61.95	1.35	94.64	91.67	2.49	0.62

Appendix

Table 7: Ablation on the inversion depth

\tau

(Algorithm 1 ) at the

20\%

target drag reduction for the Front View (Width) setting. All metrics are scaled by

\times 100

Variant	Transformer Depth	Parameters (M)
P14-D2	2	14.06
P35-D5	5	34.54
P48-D7	7	48.19
P69-D10	10	68.67
P82-D12	12	82.32

Appendix

Table 8: AnchorGen model capacity variants.

Figure 13: Target-shape metrics at $20\%$ drag reduction across AnchorGen and FCSO model capacities.

Figure 14: Shared PCA of source-centered VecSet edit features for matched AnchorGen and FCSO outputs.

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Aug 7, 2026, cs.CVJ/K move · Enter open · S save

Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models

Emilien Seiler, Nicolas Talabot, Yingxuan You, Federico Stella+1

CVLab, EPFL

Shape Optimization 3D Models Generative Models Aerodynamics Gradient-Based Optimization High-Dimensional

Open paper AskPDF arXiv

Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space. Existing mitigation strategies, including latent regularization and flow-matching approaches, either sacrifice expressiveness, demand a difficult trade-off between objective guidance and generative fidelity that remains prone to manifold drift, or are computationally infeasible to scale to modern, large-capacity 3D shape models. We introduce a novel optimizer-corrector framework that alternates between gradient steps for objective minimization and guided flow matching to drive the latent state back to the valid shape manifold. By decoupling objective minimization from flow-based correction, optimizing freely and correcting strictly, this alternating design avoids inherent trade-offs, preserving geometric validity without sacrificing expressiveness while remaining computationally feasible on modern 3D shape models. We demonstrate its effectiveness across generative priors of varying complexity, from simple vector latent spaces to large-scale architectures across a variety of downstream optimization tasks, including aerodynamic drag reduction and object compliance optimization.

Abstract

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