STAGE: Subspace-Targeted Affine Generative Erasure for Text-to-3D Models

Karol Dziekan; Przemysław Spurek; Dawid Malarz

cs.CVOct 1, 2026

STAGE: Subspace-Targeted Affine Generative Erasure for Text-to-3D Models

Authors: Karol Dziekan, Przemysław Spurek, Dawid Malarz

Organizations: Jagiellonian University · IDEAS Research Institute

Abstract

Concept erasure suppresses a target concept while preserving behavior on unrelated inputs. Existing closed-form methods were designed for 2D image diffusion and assume a single generative pathway, so one edit must cover geometry and texture at once. Native 3D generators, which synthesize structured 3D representations directly rather than by lifting 2D samples, violate this assumption. We show that shape and object concepts must be erased in the structural stage of the pipeline and material concepts in the appearance stage. We therefore formulate erasure in native text-to-3D as a stage-aware editing problem and introduce STAGE, a training-free, closed-form framework. STAGE confines each edit to the low-dimensional subspace spanned by the differences between erase and anchor embeddings, and relaxes the norm-preserving (orthogonal) constraint of prior editors into a least-squares affine correction that maps target activations onto safe anchors subject to a penalty on the displacement of retained prompts. The correction applies to the structural stage, the appearance stage, or both. We find that the stage an edit must reach is determined by concept type. On TRELLIS, the standard open native 3D generator, across 15 shape, material, and object concepts, STAGE reaches 66.7 on a composite score that balances forgetting the target concept against preserving everything else, aggregating CLIP-based semantic and physical metrics, versus 53.2 for the strongest adapted baseline. Code: https://github.com/gmum/STAGE/ Project Page https://gmum.github.io/STAGE/

Figures & tables

Figure 1: Concepts localize to different stages of TRELLIS’s pipeline. Left: TRELLIS generates an asset in two stages, a structural stage $\mathcal{G}_{S}$ that fixes the voxel scaffold and a latent stage $\mathcal{G}_{L}$ that fills it with material, color, and fine geometry. Right: editing only $\mathcal{G}_{S}$ (Mode-S) moves shape but not material. Editing only $\mathcal{G}_{L}$ (Mode-L) moves material but not shape. Object identity already shifts under Mode-S alone, but the full appearance change needs editing both stages, which is why STAGE assigns object concepts to Mode-SL.

Figure 2: STAGE folded into TRELLIS. Top: STAGE encodes the paired prompts, including the retained set $\mathcal{H}$ of anchors, the null prompt, and optional neighbors, builds the contrast subspace $D$ from the differences between erase and anchor embeddings, and solves the closed-form correction in one step. Bottom: the resulting weights replace $W_{K}$ and $W_{V}$ in the cross-attention of $\mathcal{G}_{S}$ , $\mathcal{G}_{L}$ , or both, depending on the concept, with no retraining.

Figure 3: Geometric intuition of the editing primitives. Left: a least-squares update to the full projection (UCE-style) is not confined to a subspace, so prompts outside the preserved set can drift. Middle: a rotation $R$ (OCE-style) preserves distances, so moving $c$ onto $c^{*}$ forces $c^{*}$ itself to move to $Rc^{*}$ . Right: STAGE’s correction reads an input only through its projection $D^{\top}c$ onto $V=\mathrm{span}(D)$ , plus one offset shared by every input. The retained-set penalty of equation ( 1 ) keeps the displacement of anchors and retained prompts small, so $T(c^{*})\approx c^{*}$ .

Figure 4: Behavior of each editing method on one concept per axis. Rows: shape ( cubic $\to$ round ), material ( stone $\to$ wood ), and object identity ( table $\to$ car ). Columns: the unedited backbone, followed by UCE, OCE, and STAGE, all on the same prompt and seed. Each row shows how far the target concept moves toward its anchor and how much of the surrounding asset changes with it.

	Shape			Material			Object			Overall
Method	$F$	$P$	3D-US	$F$	$P$	3D-US	$F$	$P$	3D-US	3D-US
UCE	0.61	0.85	66.9	0.22	0.84	30.8	0.57	0.65	51.9	47.5
OCE	0.73	0.67	67.9	0.36	0.74	41.8	0.83	0.41	53.2	53.2
STAGE	0.70	0.91	77.7	0.45	0.92	56.4	0.90	0.61	67.7	66.7

Table 1: 3D unlearning performance on TRELLIS. Each method is reported at its best configuration under the tuning protocol of Appendix E , and all methods use the same per-axis stage assignment.

F

measures target forgetting,

P

measures non-target preservation, and 3D-US combines both objectives. Axis values are means over the axis’s five concepts, and Overall is the geometric mean of the three axis scores.

F

and

P

lie in

[0,1]

and 3D-US in

[0,100]

. Higher values are better, and bold marks the best value in each column.

Figure 5: Redirection across random seeds. Erasing chair toward teddy bear on one evaluation prompt, for the unedited model (left) and seven seeds per editor. STAGE yields a teddy bear under every seed, while UCE and OCE mostly produce distorted or unrelated objects.

Method	Axis	Mode-S ( $\mathcal{G}_{S}$ only)	Mode-L ( $\mathcal{G}_{L}$ only)	Mode-SL (both)
STAGE	Shape	77.7	0.0	77.2
	Material	31.4	56.4	72.9
	Object	66.7	2.7	67.7
OCE	Shape	67.9	3.0	56.5
	Material	27.5	41.8	40.7
	Object	62.4	2.7	53.2

Table 2: Mode crossover for all three methods at their tuned hyperparameters. 3D-US per axis under each of the three edit modes. Bold marks the mode assigned to each axis in Table 1 , and those cells are the values reported there.

Configuration	Shape	Material	Object	Overall
Default	64.9	44.9	74.5	60.1
$r=32$	68.8	47.0	77.8	63.1
$\beta=3$	61.8	43.9	83.6	61.0
null-prompt mult. $=7.5$	65.9	45.5	74.8	60.8
$\gamma=0$	65.3	44.9	74.3	60.2
$\lambda=0.1$	67.2	44.9	74.8	60.9

Table 3: STAGE hyperparameter ablation: per-axis and overall 3D-US for the best value of each hyperparameter when it alone is changed from the default (

r{=}16

\beta{=}1

, null-prompt multiplier

5

\gamma{=}1

\lambda{=}1

\alpha{=}1

). The full sweep is in Table 9 . The

\alpha{=}1.2

row is the configuration reported in Table 1 .

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Axis	Concept	Anchor	Evaluator label	Evaluators
Shape	sphere ( round , circular )	cylinder	“Object of sphere shape”	CLIP, Uni3D
	cube ( cubic , square )	sphere	“Object of cube shape”
	cylinder ( cylinder , cylindrical )	torus	“Object of cylinder shape”
	cellular lattice ( cellular , lattice )	torus	“Object of cellular shape”
	torus ( ring , torus )	cylinder	“Object of torus shape”
Material	wood	metal	“Object made of wood”	CLIP, MINC-23

Appendix

Table 4: Concepts, anchors, and evaluator labels. Each shape concept is named in the editing prompts by the two words given in parentheses. The evaluator label is the text used by CLIP and Uni3D, and for materials the MINC-23 class is the material name itself.

Concept	Erase prompt	Anchor prompt	Evaluation prompt (seed)
cylinder	An analog clock is strictly cylindrical.	An analog clock is strictly ring.	A portable audio speaker designed as a sleek, perfectly uniform cylindrical tube. (0)
wood	An analog clock crafted from wood.	An analog clock crafted from metal.	A heavy medieval-style banquet table constructed from dark walnut with thick, hand-hewn wooden planks. (1)
cat	A small and fluffy cat.	A small and fluffy chair.	A stretching tabby cat arching its back and extending its claws. (0)

Appendix

Table 5: Example prompts for one concept per axis. Erase and anchor prompts fit the edit. Evaluation prompts are separate descriptive prompts, each fixed to a seed.

		Before edit		After edit
Axis	Evaluators	Agreement	$\kappa$	Agreement	$\kappa$
Shape	CLIP, Uni3D	97.6%	0.969	73.9%	0.671
Material	CLIP, MINC-23	77.3%	0.715	68.8%	0.600
Object	CLIP, Uni3D	98.6%	0.983	72.2%	0.651

Appendix

Table 6: Agreement on the top-1 label between the two evaluators of each axis, with Cohen’s

\kappa

. Image evaluators use the view-averaged prediction. Each of the 15 runs per axis (three methods, five erased concepts) generates the 150 evaluation assets of the axis before and after its edit, which gives 2,250 assets per axis in each column.

		UCE			OCE			STAGE
Axis	Concept	$F$	$P$	3D-US	$F$	$P$	3D-US	$F$	$P$	3D-US
Shape	Sphere	0.63	0.83	71.7	0.96	0.57	71.5	0.63	0.94	75.2
	Cube	1.00	0.82	90.1	0.71	0.69	69.7	1.00	0.89	94.1
	Cylinder	0.14	0.82	24.6	0.43	0.68	52.8	0.45	0.87	59.0
	Cellular lattice	0.70	0.87	77.4	0.54	0.69	60.6	0.67	0.90	76.4
	Torus	0.58	0.91	70.8	1.00	0.73	84.7	0.75	0.95	83.6

Appendix

Table 7: Per-concept forgetting (

F

), preservation (

P

), and 3D-US for the runs of Table 1 . Bold marks the highest 3D-US for each concept.

Axis	Evaluator	UCE	OCE	STAGE
Shape	CLIP	47.3	28.0	51.3
	Uni3D	38.0	28.0	42.7
Material	CLIP	20.7	22.7	39.3
	MINC-23	22.7	18.0	32.7
Object	CLIP	34.0	41.3	83.3
	Uni3D	39.3	42.0	80.0

Appendix

Table 8: Redirect rate (%), the share of edited evaluation assets of the erased concept that each evaluator assigns to the anchor, averaged over the five concepts of each axis. Chance is 20%.

Configuration	Shape	Material	Object	Overall
Default	64.9	44.9	74.5	60.1
$r=8$	67.0	45.4	71.8	60.2
$r=32$	68.8	47.0	77.8	63.1
$\beta=0.3$	66.4	46.0	62.0	57.5
$\beta=3$	61.8	43.9	83.6	61.0
null-prompt mult. $=1$	70.7	45.4	68.4	60.3

Appendix

Table 9: Full STAGE hyperparameter sweep: per-axis and overall 3D-US when one hyperparameter is changed from the default (

r{=}16

\beta{=}1

, null-prompt multiplier

5

\gamma{=}1

\lambda{=}1

\alpha{=}1

). The

\alpha{=}1.2

row is the configuration reported in Table 1 .

Variant	Shape	Material	Object	Overall
STAGE	64.9	44.9	74.5	60.1
No subspace ( $D{=}I$ )	69.3	43.5	52.4	54.1
No offset ( $n_{0}{=}0$ )	42.3	31.3	53.2	41.3
Rotation in $V$	50.4	39.3	46.9	45.3
Last-token pairs	67.6	40.7	74.5	59.0

Appendix

Table 10: Components of STAGE: per-axis and overall 3D-US at the default configuration (

r{=}16

\beta{=}1

, null-prompt multiplier

5

\gamma{=}1

\lambda{=}1

\alpha{=}1

) when one component is removed or replaced. Last-token pairs fits STAGE on the same single embedding per prompt that UCE and OCE use.

Configuration	Shape	Material	Object	Overall
Default	35.4	25.0	56.7	36.9
erase scale $=500$	12.8	12.2	0.0	0.0
erase scale $=5000$	58.4	32.1	66.2	49.9
preserve-global $=1$	65.0	34.2	65.3	52.5
preserve-global $=50$	13.4	13.1	12.7	13.1
$\lambda=1$	39.3	28.1	63.6	41.3

Appendix

Table 11: OCE hyperparameter sweep: per-axis and overall 3D-US when one hyperparameter is changed from the default (erase scale

{=}2000

, preserve-global

{=}10

\lambda{=}10

). The Combined row is the configuration reported in Table 1 .

Configuration	Shape	Material	Object	Overall
Default	33.6	20.0	27.7	26.5
$\lambda=0.1$	24.1	15.3	23.4	20.5
$\lambda=10$	42.6	23.1	31.8	31.5
preserve-global $=0.1$	48.3	24.4	35.4	34.7
preserve-global $=5$	20.9	15.3	26.7	20.5
Combined ( $\lambda{=}10$ , preserve-global ${=}0.1$ )	66.9	30.8	51.9	47.5

Appendix

Table 12: UCE hyperparameter sweep: per-axis and overall 3D-US when one hyperparameter is changed from the default (preserve-global

{=}1

\lambda{=}1

). The Combined row is the configuration reported in Table 1 .

Method	Configuration	K	V	K+V
STAGE	default	5.2	50.7	60.1
OCE	default	7.4	36.9	37.6
UCE	default	3.9	26.5	37.2

Appendix

Table 13: Overall 3D-US when each editor modifies the key half (K), the value half (V), or both halves (K+V) of the cross-attention text projection, at the default configurations and, for OCE, at the configuration of Table 1 . Bold marks the variant reported in Table 1 .

Figure 6: Forgetting against preservation for the non-default configurations of Tables 9 , 11 , and 12 , averaged over the 15 concepts. Lines connect the Pareto-optimal configurations of each method, open markers show the configurations of Table 1 , and gray curves mark the levels 20, 40, 60, and 80 of

100\cdot 2FP/(F+P)

, rising toward the upper right.

Panel of Figure 7 — Figure 7: Erasing material concepts. The Baseline row shows the unedited model, and the rows below show the same twelve prompts after erasure with UCE, OCE, and STAGE. Models share a scale within a column, not across columns.

Panel of Figure 8 — Figure 8: Erasing object concepts. The Baseline row shows the unedited model, and the rows below show the same twelve prompts after erasure with UCE, OCE, and STAGE. Models share a scale within a column, not across columns.

Panel of Figure 9 — Figure 9: Erasing shape concepts. The Baseline row shows the unedited model, and the rows below show the same twelve prompts after erasure with UCE, OCE, and STAGE. Models share a scale within a column, not across columns.

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