All Roads Lead to Rome: Flow-driven Multi-Anchor Exploration for Open-Environment Active 3D Mapping

Yang Li; Aming Wu; Zihao Zhang; Ziju Han; Sijia Zhang; Yahong Han

cs.ROSep 29, 2026

All Roads Lead to Rome: Flow-driven Multi-Anchor Exploration for Open-Environment Active 3D Mapping

Authors: Yang Li, Aming Wu, Zihao Zhang, Ziju Han, Sijia Zhang, Yahong Han

Organizations: School of Artificial Intelligence, Tianjin University, China · School of Computer Science and Information Engineering, Hefei University of Technology, China

Abstract

To advance the development of embodied intelligence, Open-Environment Active 3D Mapping has attracted increasing attention, aiming to perform a long-horizon and shortest trajectory exploration for reconstructing unseen scenarios. Since only limited information about unseen environments is available, methods built on the closed-set assumption, i.e., assuming that the test environments are similar to those seen during training, cannot generalize satisfactorily. In existing active mapping methods, long-horizon exploration is often guided by predicting a coarse long-range goal and then converting it into an executable path. However, this stage is usually formulated as single-point prediction. Under partial observability, the same local observation may correspond to multiple plausible exploration directions, making such deterministic prediction prone to brittle decisions and degraded performance in unseen scenarios. Our experiments further verify that this is a key factor underlying their weak generalization. To address this issue, we reformulate long-horizon target prediction as conditional multimodal anchor generation using Conditional Flow Matching.Instead of predicting a single goal, our method learns a conditional distribution over coarse exploration anchors from the current mapping state. These anchors are first converted into executable candidate paths through obstacle-aware planning. We then apply exploration-mode clustering to compress geometrically similar trajectories and reduce candidate redundancy. Finally, a hierarchical selection module selects the most promising mode and reranks paths within it to produce the final executable trajectory. Experiments show that our method improves generalization and reconstruction efficiency in open environments.

Figures & tables

Figure 1 : Motivation. Under partial observability, a similar local observation may support multiple plausible long-horizon exploration directions. Single-goal prediction collapses these futures into one dominant branch and generalizes poorly when the unseen scene continuation changes. In contrast, multimodal anchor modeling preserves alternative hypotheses before downstream planning, leading to better generalization and higher coverage.

Figure 2 : Conditional Flow Matching for multimodal long-horizon anchors. CFM transports samples from a simple prior $x_{0}\sim\mathcal{N}(0,I)$ toward the target anchor distribution $x_{1}\sim p_{1}(\cdot\mid z_{t})$ , yielding multiple plausible long-horizon exploration hypotheses under the same partial observation. Unlike directly generating full trajectories, this formulation models coarse exploration intent in a compact space and remains naturally compatible with downstream planning.

Figure 3 : Overview of our method. Given the current mapping state $E_{t}$ , a mapping-progress encoder produces the context feature $z_{t}$ . Conditional Flow Matching (CFM) then generates a multimodal set of long-horizon exploration anchors $\mathcal{A}_{t}$ , which are converted into executable candidate paths and clustered into exploration modes $\{\mathcal{M}_{t}^{(m)}\}_{m=1}^{M_{t}}$ . Finally, a hierarchical selection module first selects the most promising mode and then reranks paths within that mode to output the final trajectory $\tau_{t}^{\star}$ .

	Simple		Normal		Hard		Insane
	Final Cov.	AUCs	Final Cov.	AUCs	Final Cov.	AUCs	Final Cov.	AUCs
Random	0.323 ±0.156	0.270 ±0.135	0.190 ±0.124	0.152 ±0.103	0.124 ±0.082	0.088 ±0.060	0.074 ±0.048	0.050 ±0.035
FBE [ 18 ]	0.760 ±0.174	0.605 ±0.171	0.565 ±0.139	0.415 ±0.109	0.425 ±0.114	0.311 ±0.080	0.330 ±0.097	0.239 ±0.079
SCONE [ 19 ]	0.577 ±0.173	0.483 ±0.138	0.412 ±0.114	0.313 ±0.087	0.290 ±0.093	0.210 ±0.072	0.196 ±0.079	0.140 ±0.060
MACARONS [ 7 ]	0.599 ±0.200	0.479 ±0.172	0.418 ±0.120	0.314 ±0.088	0.302 ±0.097	0.218 ±0.070	0.192 ±0.078	0.139 ±0.058
NBP [ 8 ]	0.879 ±0.142	0.692 ±0.156	0.734 ±0.142	0.526 ±0.112	0.618 ±0.153	0.432 ±0.115	0.472 ±0.095	0.312 ±0.073

Table 1 : Evaluation results on AiMDoom Dataset. For each difficulty level, all baseline models, including ours, are trained from scratch on the corresponding training set to ensure a fair comparison.

Method	Comp. (%) $\uparrow$	Comp. (cm) $\downarrow$
Random	45.67	26.53
FBE [ 18 ]	71.18	9.78
UPEN [ 3 ]	69.06	10.60
OccAnt [ 6 ]	71.72	9.40
ANM [ 4 ]	73.15	9.11
NBP [ 8 ]	79.38	6.78

Table 2 : Comparison on the MP3D dataset.

Method	Comp. (%) $\uparrow$	Comp. (cm) $\downarrow$
Random	32.12	29.36
FBE [ 18 ]	56.73	14.45
UPEN [ 3 ]	54.70	13.09
OccAnt [ 6 ]	58.49	14.18
ANM [ 4 ]	60.22	11.78
NBP [ 8 ]	61.81	10.22

Table 3 : Train on AiMDoom test on MP3D.

Figure 4 : Qualitative comparison between the SOTA method NBP (Top) and Ours (Bottom). For each scene, both methods start from the same initial pose. The dashed boxes highlight representative regions that remain unexplored by NBP but are successfully recovered by our method. This difference is not merely local: NBP tends to commit early to a single dominant long-horizon branch, which induces a narrower global coverage pattern and leaves weakly indicated but still informative continuations unexplored. In contrast, our method preserves multiple plausible long-horizon exploration hypotheses before downstream planning and selection, enabling more balanced expansion across alternative scene continuations and ultimately yielding more complete scene coverage.

Protocol A: Train on Simple, test on all difficulty levels
		Simple		Normal		Hard		Insane
Protocol	Method	Final Cov.	AUC	Final Cov.	AUC	Final Cov.	AUC	Final Cov.	AUC
	Random	0.323 $\pm$ 0.156	0.270 $\pm$ 0.135	0.174 $\pm$ 0.112	0.132 $\pm$ 0.091	0.101 $\pm$ 0.075	0.072 $\pm$ 0.054	0.062 $\pm$ 0.041	0.041 $\pm$ 0.030
	FBE [ 18 ]	0.760 $\pm$ 0.174	0.605 $\pm$ 0.171	0.512 $\pm$ 0.155	0.364 $\pm$ 0.124	0.368 $\pm$ 0.132	0.255 $\pm$ 0.098	0.284 $\pm$ 0.110	0.188 $\pm$ 0.088
	SCONE [ 19 ]	0.577 $\pm$ 0.173	0.483 $\pm$ 0.138	0.354 $\pm$ 0.128	0.245 $\pm$ 0.104	0.213 $\pm$ 0.111	0.142 $\pm$ 0.082	0.145 $\pm$ 0.092	0.094 $\pm$ 0.071
	MACARONS [ 7 ]	0.599 $\pm$ 0.200	0.479 $\pm$ 0.172	0.368 $\pm$ 0.141	0.252 $\pm$ 0.115	0.225 $\pm$ 0.124	0.148 $\pm$ 0.087	0.151 $\pm$ 0.096	0.098 $\pm$ 0.075

Table 4 : Generalization under difficulty shift on AiMDoom. We report two complementary protocols. Protocol A evaluates cross-difficulty transfer by training on the Simple split only and directly testing on all difficulty levels . Protocol B evaluates leave-one-difficulty-out generalization by training on Simple + Normal + Hard and directly testing on the held-out Insane split.

Method				OOD Setting
Baseline	MAG	EMC	HMS	Comp. (%) $\uparrow$	Comp. (cm) $\downarrow$
$\checkmark$				61.81	10.22
$\checkmark$	$\checkmark$			66.21	9.64
$\checkmark$	$\checkmark$	$\checkmark$		67.60	9.36
$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	68.45	9.11

Table 5 : Progressive validation of the proposed pipeline under the cross-dataset OOD setting.

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3D Mapping 3D Generation

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Current 3D mapping pipelines generally assume static environments, which limits their ability to accurately capture and reconstruct moving objects. To address this limitation, we introduce the novel task of active mapping of moving objects, in which a mapping agent must plan its trajectory while compensating for the object's motion. Our approach, Paparazzo, provides a learning-free solution that robustly predicts the target's trajectory and identifies the most informative viewpoints from which to observe it, to plan its own path. We also contribute a comprehensive benchmark designed for this new task. Through extensive experiments, we show that Paparazzo significantly improves 3D reconstruction completeness and accuracy compared to several strong baselines, marking an important step toward dynamic scene understanding. Project page: https://davidea97.github.io/paparazzo-page/

Abstract

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