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

Karol Dziekan, Przemysław Spurek, Dawid Malarz

arXiv:2610.01302v1cs.CV

TL;DR

Native text-to-3D generators have structural and appearance pathways that make 2D closed-form erasure assumptions insufficient. STAGE uses stage-aware, subspace-confined affine edits, reaching 66.7 on the 3D Unlearning Score versus 53.2 for the strongest adapted baseline across 15 concepts on TRELLIS.

  • Problem

    Closed-form concept erasure was designed for 2D image diffusion, while erasing text-specified concepts from native text-to-3D generators remains largely unaddressed.

    Source: §1 · p. 2

  • Method

    STAGE fits a least-squares affine correction within the subspace of erase–anchor embedding differences and applies it to the structural stage, appearance stage, or both according to concept type.

    Source: §1 · p. 2, §3 · p. 4

  • Results

    66.7 on the 3D Unlearning Score versus 53.2 for the strongest adapted baseline across 15 shape, material, and object concepts on TRELLIS.

    Source: §5 · p. 9

  • Takeaways & Limitations

    On TRELLIS, the stage an edit must reach depends on concept type, and stage-aware editing balances concept removal and preservation in native 3D generation.

    Source: §1 · p. 2, §5 · p. 9

    Quantitative erasure evaluation depends on the pretrained generator's capabilities and available evaluators; finer-grained, domain-specific evaluation must distinguish target-attribute removal from changes to related attributes.

    Source: §5 · p. 9

Abstract

from arXiv · show

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/

1 INTRODUCTION

Erasure for native text-to-3D generators remains largely unaddressed, and their separate structural and appearance stages make 2D editing assumptions insufficient. STAGE introduces stage-aware, closed-form editing and outperforms the adapted baseline on TRELLIS.

1 INTRODUCTION

  • Text-specified concept erasure for native text-to-3D generators remains largely unaddressed, despite prior work on image-to-3D models and 2D diffusion.Native generators directly synthesize structured 3D representations, while the cited prior 3D unlearning work fine-tunes an image-to-3D model.Source: §1 · p. 2
  • Shape and object concepts depend on structural processing, while material concepts are erased more effectively in the appearance stage and most completely when both stages are edited.Editing a stage that does not carry the target concept can cause collateral change; structural changes can propagate through the scaffold into appearance.Source: §1 · p. 2
  • STAGE is a training-free, closed-form framework that confines edits to erase–anchor embedding differences and fits an affine correction penalizing displacement of retained prompts.The correction can be folded into the structural stage, appearance stage, or both according to concept type.Source: §1 · p. 2
  • 66.7 on the 3D Unlearning Score versus 53.2 for the strongest adapted baseline across 15 shape, material, and object concepts on TRELLIS.The score aggregates CLIP-based semantic and physical metrics.Source: §1 · p. 2

2 RELATED WORK

Prior concept-erasure work includes inference-time steering, fine-tuning, and closed-form edits developed for 2D image diffusion. Native 3D generators pose distinct editing and evaluation needs because their structural and appearance stages produce a 3D asset.

2 RELATED WORK

  • Concept-erasure methods include inference-time steering or projection, objective-based fine-tuning, and closed-form edits to text-conditioning layers.Examples in the passage include Safe Latent Diffusion and AdaVD, ESD and later fine-tuning approaches, and UCE, RECE, and OCE.Source: §2 · p. 2
  • OCE uses a distance-preserving rotation that cannot map an erased concept to a distinct anchor while leaving that anchor fixed; STAGE instead uses a subspace-confined affine correction.Unlike STAGE, UCE's least-squares update is unconstrained.Source: §2 · p. 3
  • The prior 3D-unlearning approach described fine-tunes the image-to-3D pipeline's front-end multi-view diffusion model, leaving downstream reconstruction untouched.STAGE edits text-conditioning layers of a native 3D generator, including its structural stage.Source: §2 · p. 3
  • Rendered-view metrics alone depend on camera choice and cannot distinguish geometry changes from appearance changes in a 3D asset.The proposed 3D Unlearning Score combines rendered-view CLIP scores with point-cloud or material-classifier evaluation and measures preservation against the unedited model.Source: §2 · p. 3

3 METHOD

STAGE edits text-conditioned cross-attention in TRELLIS's cascaded structural and appearance stages, assigning stages by concept type. It uses paired erase–anchor embeddings to fit a subspace-confined affine correction, then folds that correction into selected layers without retraining.

3 METHOD

  • The fitted correction folds exactly into cross-attention projections, replacing their key and value weights in the structural stage, appearance stage, or both without retraining.The same text-derived correction is reused for every layer into which the edit is folded.Source: Figure 2 · p. 3, §3 · p. 5
  • TRELLIS first builds a geometric scaffold in its structural stage, then generates appearance and fine local geometry on that support; the stages read the same text embedding independently.STAGE assigns shape edits to the structural stage, material edits to the appearance stage, and object edits to both.Source: §3 · pp. 3–4
  • The editing goal is to make prompts built around each erased concept produce the representation of its safe anchor while preserving behavior on unrelated concepts.STAGE edits the fused key and value projections together in each selected cross-attention block.Source: §3 · pp. 3–4
  • In the cascaded architecture, an unnecessary structural-stage change can alter voxel support and thereby change the appearance generated downstream.This motivates restricting edits to stages that carry the target concept and confining their effects to a small subspace.Source: §3 · p. 4
  • Template-parallel erase and anchor prompts differ in the concept word, and aligned token-state differences define a data-driven subspace for the correction.The default subspace uses 16 dimensions out of embedding width 768; each input is changed through its projection onto that subspace plus a shared offset.Source: §3 · p. 4
  • STAGE's affine correction acts through the erase–anchor subspace plus a shared offset, unlike a rotation that preserves distances or an unconstrained full-projection update.The figure contrasts these primitives and shows the retained-set penalty keeping anchor and retained-prompt displacement small.Source: §3 · p. 4, Figure 3 · p. 5
  • Regularized least squares fits the correction to map erase embeddings onto anchors while minimizing movement of retained anchors, the null prompt, and optional neighbors.The null prompt receives greater weight because classifier-free guidance amplifies its drift.Source: §3 · p. 4
  • A corpus-level second-moment regularizer discourages corrections aligned with unusually high-variance prompt directions, and a strictly convex objective yields a unique closed-form solution.The solution requires one small (r+1)×(r+1) linear solve, independent of embedding width, and is reused across layers.Source: §3 · pp. 4–5

4 EXPERIMENTS

Experiments evaluate STAGE on TRELLIS across 15 shape, material, and object concepts, finding that its strongest edit stage depends on concept type. STAGE leads the reported composite erasure-and-preservation results, with ablations and sweeps probing its design and tuning.

Evaluation

  • The 3D Unlearning Score combines target forgetting and non-target preservation, using semantic and axis-specific physical evaluators to assess 3D erasure.The concept-level score is the harmonic mean of forgetting and preservation, and the three axis scores are summarized by their geometric mean.Source: §4 · p. 6

Main Results

  • STAGE attains the highest 3D-US on every axis and overall, leading OCE by at least 9.8 points on every axis and scoring highest on 10 of 15 concepts.It keeps preservation above 0.84 on every shape and material concept; object preservation is harder for all methods.Source: Table 1 · p. 7, §4 · p. 7
  • The reported result is 30.0% for OCE, and performance is at least 80% on the object axis (Appendix D).Source: §4 · p. 8

Mode Assignment and Stage Locality

  • Mode tests support structural-stage edits for shape and object concepts and appearance-stage edits for materials, with both stages improving material erasure.For STAGE, shape and object 3D-US are 77.7 and 66.7 with GS only, versus 0.0 and 2.7 with GL only; material scores are 56.4 with GL only, 31.4 with GS only, and 72.9 with both.Source: Table 2 · p. 8, §4 · p. 8

Hyperparameter Sweeps

  • Across the full STAGE hyperparameter sweep, overall 3D-US stays between 57.5 and 63.1, above OCE’s best tuned 53.2; α is the only parameter with a large effect.Overall 3D-US peaks at α=1.2; combining α=1.5 with r=32 gives 66.2, no better than α=1.2 alone.Source: §4 · p. 9

Ablations

  • Removing the subspace or offset, or using a rotation, lowers default overall 3D-US from 60.1 to between 41.3 and 54.1; last-token fitting scores 59.0.These are ablation results on all 15 concepts.Source: Table 3 · p. 9, §4 · p. 9

5 CONCLUSION

STAGE is a training-free, closed-form framework for stage-aware concept erasure in native text-to-3D generation. On TRELLIS, results support stage-aware editing as an effective balance between concept removal and preservation, while evaluation scope remains bounded by the generator and available evaluators.

5 CONCLUSION

  • 66.7 versus 53.2 for the strongest adapted baseline on the 3D Unlearning Score across 15 shape, material, and object concepts.The comparison uses the same stage assignment for all editors.Source: §5 · p. 9
  • The stage an edit must reach depends on concept type, and STAGE combines a subspace derived from erase–anchor embedding differences with an affine correction.The framework enables targeted weight edits without additional inference cost.Source: §5 · p. 9
  • Quantitative erasure evaluation is limited by the pretrained generator’s capabilities and the available evaluators.Finer-grained and domain-specific evaluation must distinguish removal of a target attribute from changes to closely related attributes.Source: §5 · p. 9

A CONCEPTS AND PROMPT CONSTRUCTION

The evaluation covers 15 concepts across shape, material, and object axes, pairing each with a same-axis safe anchor. Editing prompts are separated from evaluation prompts, which are screened to ensure TRELLIS expresses each target concept.

A CONCEPTS AND PROMPT CONSTRUCTION

  • The study evaluates 15 concepts, five per axis, each paired with a safe anchor from the same axis; Table 4 lists anchors and evaluator labels.Shape concepts are named by two prompt words, while the evaluator labels are used by CLIP and Uni3D and, for materials, the MINC-23 class names.Source: A CONCEPTS AND PROMPT CONSTRUCTION · p. 12, Table 4 · p. 12
  • Each concept has 120 template-parallel erase and anchor prompt pairs that differ only in the concept word, and these prompts are not used for evaluation.Shape concepts use two names; when token counts differ, STAGE pairs only final token positions where both states encode the full prompt.Source: A CONCEPTS AND PROMPT CONSTRUCTION · p. 12
  • Evaluation prompts are separate descriptive asset prompts, and each concept’s candidates are seed-searched until 30 prompt–seed pairs are accepted.A pair is accepted only when every evaluator for that axis assigns the generated asset to the target concept; methods and ablations reuse the accepted pairs and seeds.Source: A CONCEPTS AND PROMPT CONSTRUCTION · pp. 12–13
  • The caption second moment K0 is computed once from 30,000 ObjaverseXL captions encoded with TRELLIS’s conditioning CLIP ViT-L/14 encoder.All three editors use the same K0.Source: A CONCEPTS AND PROMPT CONSTRUCTION · p. 13
  • Adding a concept requires selecting a same-axis anchor and evaluator label, constructing paired prompts, finding 30 accepted evaluation pairs, and meeting the pre-edit detection threshold.Table 5 separates the erase and anchor prompts used to fit edits from the fixed-seed evaluation prompts.Source: A CONCEPTS AND PROMPT CONSTRUCTION · p. 13, Table 5 · p. 13

B IMPLEMENTATION OF THE EDITORS

The editors share prompts, caption statistics, selected TRELLIS stages, generation settings, and evaluation code; they differ in the update they compute. STAGE uses aligned token states and a subspace-confined affine correction, while UCE uses a least-squares update and OCE uses a rotation.

B IMPLEMENTATION OF THE EDITORS

  • All three editors use the same 120 erase–anchor prompt pairs, caption statistic K0, selected-stage cross-attention projections, generation pairs, and evaluation code.The shared pipeline provides no additional preservation prompts; the editors use the frozen CLIP ViT-L/14 encoder and update 28 layers per selected stage.Source: B IMPLEMENTATION OF THE EDITORS · p. 13
  • UCE maps erase embeddings to the mean anchor embedding and preserves caption-corpus token states, using the same key-and-value projections and ridge regularization as its implementation.Its preserve-set statistic is based on the TRELLIS caption corpus rather than an explicit list of concepts.Source: B IMPLEMENTATION OF THE EDITORS · pp. 13–14
  • OCE seeks an orthogonal rotation mapping erase images to anchor images while preserving other concepts, but this setup omits its explicit neighboring-concept list.The adaptation uses the TRELLIS caption corpus for K0 and adds a ridge term; setting λ to zero gives an overall 3D-US of 52.1, close to the 53.2 reported in Table 1.Source: B IMPLEMENTATION OF THE EDITORS · p. 14
  • OCE obtains its rotation from the SVD of an objective matrix, with the erase term driving change while the positive-semidefinite K0 and ridge terms keep the rotation near identity.The swept parameters include erase scale, preserve-global weight, and ridge weight.Source: B IMPLEMENTATION OF THE EDITORS · p. 14
  • STAGE uses aligned token states and folds its correction into both the weights and bias of each selected projection.It pairs all aligned positions for equal-length prompts, drops coincident states, and pairs later positions when token counts differ; its retained set includes anchor states and empty-prompt states.Source: B IMPLEMENTATION OF THE EDITORS · p. 14

C EVALUATION PROTOCOL

The evaluation combines rendered-view and 3D or material evidence, with evaluators chosen for each concept axis. Evaluator agreement is substantial, and STAGE’s first-place ranking persists under alternative score aggregations.

C EVALUATION PROTOCOL

  • Assets are rendered from TRELLIS’s Gaussian output at four camera positions, and Uni3D point clouds use 10,000 sampled Gaussian centers.The point clouds retain centers with opacity above 0.1 and are normalized to zero mean and unit radius.Source: C EVALUATION PROTOCOL · p. 15
  • CLIP evaluates rendered views across all axes, while shape and object concepts also use Uni3D point clouds and material concepts use a restricted MINC-23 classifier.The physical evaluator differs by concept axis, and all evaluators use the same five-label candidate set and chance level.Source: C EVALUATION PROTOCOL · p. 15
  • Detection is top-1 target recognition across views for CLIP and MINC-23 and a single point-cloud prediction for Uni3D; preservation compares alignment with the prompt against other axis labels.For MINC-23, preservation uses the chance-corrected probability of the asset’s own material.Source: C EVALUATION PROTOCOL · p. 15
  • 69–74% evaluator agreement, with Cohen’s κ between 0.60 and 0.67, was observed on edited generations; STAGE ranked first under several alternative score aggregations.The ranking remained ahead of OCE and UCE by at least 11 points under the reported alternatives.Source: C EVALUATION PROTOCOL · p. 15, Table 6 · p. 15

D DETAILED RESULTS

The detailed results report per-concept 3D-US and test whether erased concepts are redirected to their intended anchors. STAGE leads on most concepts and redirects assets to anchors more often than either baseline.

Per-Concept Scores

Redirection to the Anchor

  • Across every axis and evaluator, STAGE reaches the anchor more often than both baselines; chance is 20%.Redirect rate is the share of edited assets whose top-1 label becomes the erased concept’s anchor.Source: D DETAILED RESULTS · p. 16, Table 8 · p. 16
  • Image evaluators use view-averaged predictions for redirection, while forgetting uses an any-view rule that can assign multiple labels to one asset.The any-view rule suits detection because a concept visible from one view still counts as present.Source: D DETAILED RESULTS · p. 16

E ABLATIONS

The ablations examine STAGE’s hyperparameters, components, and projection choices, alongside forgetting-preservation trade-offs. They show that the offset and subspace confinement matter, while value-projection edits outperform key-only edits.

STAGE Hyperparameter Sweep

  • STAGE’s reported configuration changes only overshoot to α=1.2; combining a larger overshoot with the best other hyperparameter (α=1.5, r=32) does not improve it.The one-at-a-time sweep evaluates configurations across all 15 concepts.Source: E ABLATIONS · p. 17, Table 9 · p. 17

Components of STAGE

  • Removing the offset lowers forgetting on every axis and gives 41.3 overall 3D-US; removing subspace confinement gives 54.1, while an orthogonal map gives 45.3.Without confinement, forgetting rises on shape but preservation falls on every axis, especially object preservation (0.36 versus 0.73).Source: E ABLATIONS · p. 17, Table 10 · p. 18
  • Last-token-only fitting uses 120 prompt pairs and reaches 59.0 overall 3D-US, close to token-level pairing at 60.1 and above OCE at 53.2 and UCE at 47.5.This indicates STAGE’s advantage does not come from its additional token pairs.Source: E ABLATIONS · p. 17, Table 10 · p. 18

Edited Projections

  • At default settings, all three editors do best when value projections are edited alone or with keys, while key-only edits erase almost nothing.STAGE edits both halves; tuned OCE’s value edit scores 53.2, versus 52.1 when λ=0 restores its original objective.Source: E ABLATIONS · p. 18, Table 13 · p. 19

Forgetting and Preservation Trade-off

  • STAGE configurations form a forgetting-preservation frontier above both baselines; every baseline configuration forgetting more than 0.15 is matched or exceeded on both measures.Baseline configurations outside the frontier retain high preservation while barely changing the model.Source: E ABLATIONS · p. 19, Figure 6 · p. 19

F QUALITATIVE RESULTS

The qualitative results show twelve fixed-seed evaluation prompts for each concept across material, object, and shape axes, comparing the unedited model with UCE, OCE, and STAGE under per-axis stage assignments.

Qualitative Results

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