Online Feedback Efficient Active Target Discovery in Partially Observable Environments
Authors: Anindya Sarkar
Binglin Ji
Yevgeniy Vorobeychik
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Model
Active Target Discovery
Primary area: general_machine_learning

Abstract: In various scientific and engineering domains, where data acquisition is costly—such as in medical imaging, environmental monitoring, or remote sensing—strategic sampling from unobserved regions, guided by prior observations, is essential to maximize target discovery within a limited sampling budget. In this work, we introduce Diffusion-guided Active Target Discovery (DiffATD), a novel method that leverages diffusion dynamics for active target discovery. DiffATD maintains a belief distribution over each unobserved state in the environment, using this distribution to dynamically balance exploration-exploitation. Exploration reduces uncertainty by sampling regions with the highest expected entropy, while exploitation targets areas with the highest likelihood of discovering the target, indicated by the belief distribution and an incrementally trained reward model designed to learn the characteristics of the target. DiffATD enables efficient target discovery in a partially observable environment within a fixed sampling budget, all without relying on any prior supervised training. Furthermore,  DiffATD offers interpretability, unlike existing black-box policies that require extensive supervised training. Through extensive experiments and ablation studies across diverse domains, including medical imaging, species discovery and remote sensing, we show that DiffATD performs significantly better than baselines and competitively with supervised methods that operate under full environmental observability.

Online Feedback Efficient Active Target Discovery in Partially Observable Environments
Anindya Sarkar", Binglin Ji", Yevgeniy Vorobeychik wwweewl.eeeeeee.
fanindya, binglin.j. j, yvorobeychild wrorobeychik@@vustl...
Department of Computer Science and Engineering Washington University in St. Louis, USA
Abstract
In various scientific and engineering domains, where data acquisition is costly-suu such in medical imaging. environmental monitoring. or remote sens- ing-strategic sampling from unobserved regions, guided by prior observations, is essential to maximize target discovery within a limited sampling budget. In this work, we introduce Diffusion-guided Active Target Discovery (DiffATD). novel method that leverages diffusion dynamics for active target discovery. DiffATD maintains belief distribution over each unobserved state in the environment, ing this distribution to dynamically balance ppploration-cxploitaaei reduces uncertainty by sampling regions with the highest expected entropy. while exploitation targets areas with the highest likelihood of discovering the target, indicated by the belief distribution and incrementally trained reward model designed to learn the characteristics of the target. DiffATD enables efficient target discovery in partially observable environment within fixed sampling budget, all without relying on any prior supervised training. Furthermore, DisJATD offers interpretability, unlike existing black-box policies that require extensive supervised training. Through extensive experiments and ablation studies across diverse do- mains, including medical imaging, species discovery and remote sensing, we show that DiffATD performs significantly better than baselines and competitively with supervised methods that operate under full environmental observability.
Exploration
Introduction
A key challenge in many scientific discovery applications is the high cost associated with sampling and acquiring feedback from the ground-truth reward function, which often requires extensive resources, time, and cost. For instance, in MRI, doctors aim to minimize radiation exposure by strategically selecting brain regions identify potential tumors or other conditions. However, obtaining detailed and time-consuming, involving advanced equipment,
scans for accurate diagnosis is resource-intent skilled technicians, and substantial patient time. Furthermore, gathering reliable feedback to guide treatment decisions often requires expert judgment, adding another layer of complexity and cost. Similarly, in a search and rescue mission, personnel must strategically decide where to sample next based on prior observations to locate a target of interest (e.g., missing person), taking into account limitations such as restricted field of view and high acquisition costs. In this context, obtaining feedback from the ground truth reward function could involve sending team for on-site verification or having human analyst review the collected imagery, both of which require significant resources and expert judgment. This challenge extends to various scientific and engineering fields, such as material and drug discovery, where the objective may vary but the core problem ooptmizzin sampling to identify target under constraints remains the same. The challenge is further exacerbated by the
Equal contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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ATD Steps
Figure I: DiffATD uncovers more target pixels (c.g., plane) while exhibiting higher uncertainty in the search space. In contrast, DiffATD without exploitation explores the environment more effectively, resulting in lower entropy but identifies fewer target pixels.
fact that obtaining labeled data for certain rare target categories, such as rare tumors, often not feasible. Naturally, the question emerges: Is if possible to design an algorithm capable of identifying the target of interest while minimizing reliance on expensive ground truth feedback, and without requiring any task-specific supervised training?
The challenge is twofold: (i) the agent must judiciously sample the most informative region from a partially observed scene to maximize its understanding of the search space, and (ii) it must concurrently ensure that this selection contributes to the goal of identifying regions likely to include the target. One might wonder why the agent cannot simply learn to choose regions that directly unveil target regions, bypassing the need acquire knowledge about the underlying environment. The crux of the issue lies in the inherent complexity of reasoning within an unknown, partially observable domain. Consequently, the agent must deftly balance exploration innattioon-ienniiiiiinnn regions that yield the greatest informational gain about the search space-with cotooittttooooouusiiii on areas more likely to contain the target based on the evolving understanding of the environment. Prior approaches typically rely on off-the-shelf reinforcement learning algorithms to develop a search policy that can efficiently explore a search space and identify target regions within partially observable environment by training large-scale pre-labeled datasets from similar tasks. However, obtaining such supervised datasets often impractical in practice, restricting the models' applicability in real-world scenarios. Suppose the task is identifying rare tumor in an MRI image. In that case, it is unrealistic to expect large-scale supervised data for such a rare condition, with positive labels indicating the target.
To address this challenge, we introduce DiffATD, an approach capable of uncovering target in partially observable environment without the need for training on pre-laheled datasets, setting apart from previous methods. Conditioned on the observations gathered so far, DiffA77) leverages Tweedie's formula to construct belief distribution over each unobserved region of the search space. Exploration is guided by selecting the region with the highest expected entropy of the corresponding belief distribution, while exploitation directs attention to the region with the highest likelihood score measured by the lowest expected entropy, modulated by the reward value, predicted by an online-trained reward model designed to predict the "target-ness" of a region. Figure 1 illustrates how exploitation enables DiffATD to uncover more target pixels (c.g., plane) while exhibiting higher uncertainty about the search space. Moreover, DiffATD offers interpretability. providing enhanced transparency compared to existing methods that rely opaque black-box policies. all while being firmly grounded in the theoretical framework of Bayesian experiment design. We summarize our contributions follows:
We propose DifAATD, novel algorithm that uncovers the target of interest within feed- back/query budget partially observable environment, minimizing reliance on costly ground truth feedback and avoiding the need for task-specific training with annotated data. DiffATD features a white-box policy for sample selection based on Bayesian experiment design, offering greater interpretability and transparency compared existing black-box methods.
We demonstrate the significance of each component in our proposed DiffATD method through extensive quantitative and qualitative ablation studies across range of datasets, including medical imaging, species distribution modeling, and remote sensing.

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2 Related Work
Active Target/Scene Reconstruction. There is extensive prior work active reconstruction of scenes and/or objects 2 Recently, deep learning methods have been developed to design subsampling strategies that aim minimize reconstruction error. Fixed strategies, such as those proposed by [4,5] involve designing a single sampling mask for a specific domain, which is then applied uniformly to all samples during inference. While effective in certain scenarios, these methods face limitations when the optimal sampling pattern varies across individual samples. To overcome have been introduced, dynamically tailoring sampling strategies to each sample during inference. [6] trained a neural network to iteratively construct an acquisition mask of M k-space lines, adding lines adaptively based on the current reconstruction and prior context. Similarly, 7 used an RL agent for this process. However, these methods rely on black- box policies, making failure cases hard interpret. Generative approaches. like [10] [I] address this with transparent sampling policies, such as maximum-variane sampling for measurement selection. However, all these prior methods typically focus solely on optimizing for reconstruction, while our ultimate goal is identifying target-rich regions. Success for our task hinges on balancing exploration (obtaining useful information about the scene) and exploitation (uncovering targets).
this, aampleaddativee approaches 66
8
9
Learning Based approaches for Active Target Discovery. Several RL-based approaches, such as [12 [3 15), have been proposed for active target discovery, but these methods rely on full observability of the search space and large-scale pre-labeled datasets for learning an efficient sub- sampling strategy. Training-free methods inspired by Bayesian decision theory offer promising approach to active target discovery 18) However, their reliance on full observability of the search space remains a significant limitation, rendering them ineffective in scenarios with partial observability. More Recently, series of methods, such as 19 active discovery in partially observable environments. Despite their potential, these approaches face a significant hurdle the reliance on extensive pre-labeled datasets to fully realize their capabilities. In this work, we present a novel algorithm, DifJATD, designed to overcome the limitations of prior approaches by enabling efficient target discovery in partially observable environments. DiffATD elim- inates the need for pre-labeled training data, significantly enhancing its adaptability and practicality across diverse applications, from medical imaging to remote sensing.
20 21]. have been proposed to tackle
3 Preliminaries
Denoising diffusion models trained to reverse Stochastic Differential Equation (SDE) that gradually perturbs samples x into a standard normal distribution [2].. The SDE governing the noising process is given by:
dr B(T) x dr + v B(T du
where zu E Idd is an initial clean sample, T). 3(T) is the noise schedule, and is standard Wiener process, with x(T') (O, 1). According [23]. this SDE can be reversed once the score function v (xr) is known, where t is a standard Wiener process running backwards:
B(T) r B(T) (x) dr + v B((F)dd) di
dr
Following 24 25 the discrete formulation of the SDE is defined as I, x(TT/N), 3 3(rT/N), ar
Br, and ā II=_1 agg. where N represents the number of discretized segments. The diffusion model reverses the SDE by learning the score function using neural network parameterized by 0, where so (Ir,, r) R V,, pr The reverse diffusion process can be conditioned on observations gathered so far yt to generate samples from the posterior p(a: yr). This achieved by substituting Vz, log P+ (x+) with the conditional score function V., log P= yt) in the above Equation. The difficulty in handling Va, log (ye ), stemming from the application of Bayes' rule to refactor the posterior, has inspired the creation of several approximate guidance techniques [26] (27 to compute these gradients with respect to partially noised sample z,. Most of these methods utilize Tweedie's 's formula, which serves as a one-step denoising operation from T - 0. represented as Tx(.). Using a trained diffusion model, the fully denoised sample zy can be estimated from its noisy version 2, as follows:
to = Ta (x(x)) = Var
(Ir + (1 az (EF))()TTTT))))
3

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Problem Formulation
In this section, we present the details of our proposed Active Target Discovery (ATD) task setup. ATD involves actively uncovering one more targets within search area, represented as region divided into N grid cells, such that æ = (x(2), x "..,,,,..",.)))) x(N).. ATD operates under a query budget B, representing the maximum number of measurements allowed. Each grid cell represents sub-region and serves as potential measurement location. A measurement reveals the content of a specific sub-region 2((() for the i-th grid cell, yielding an outcome y() E [0, 1], where y( represents the ratio of pixels in the grid cell x(9) that belongs to the target of interest. In each task configuration, the target's 's content is initially unknown and is revealed incrementally through observations from measurements. The goal is to identify as many grid cells belonging to the target as possible by strategically exploring the grid within the given budget B. Denoting query performed in step yt- the overall task optimization objective is:
U(x((a)); (9+) = max
Σ
y (+)) subject to t i B
(1)
(9c)
With objective in focus, we aim to develop a search policy that efficiently explores the search area (Frest X to identify as many target regions as possible within measurement budget B, and to achieve this by utilizing a pre-trained diffusion model, trained in an unsupervised manner on samples Tuaii from the training set, Xmain-
5 Solution Approach
Crafting a sampling strategy that efficiently balances exploration and exploitation is the key to success in solving ATD. Before delving into exploitation, first explain how DiffATI tackles exploration of the search space using the measurements gathered so far. To this end, DiffATD follows a maximum-entropy strategy, by selecting measurement exp.
exp arg max [f x Qr, i.-1]] de
9t
where denotes the mutual information between the full search space x and the predicted search space ft. conditioned on prior observations (#.-1) and the measurement locations Q: {go- ........ selected up to time where di is the measurement location at time t. We now present a proposition that facilitates the simplification of Equation 2
Proposition 1. Maximizing ( x | Qt, T(-1) w.r.t measurement location qe is equivalent to maximizing the marginal entropy of the estimated search space ū i.e.,
arg max [[(5; x Rz-)) arg max (H (2, 9e
41
Where H denotes entropy. We derive Prop. [ in the Appendix. The marginal entropy ( #1-1) can be expressed as EE, [log p(,, Qu. i.]. representing the expected log- likelihood of the esti- mated search space è based on the observations collected so far and the set of measurement locations Qt- We refer to this distribution as the belief distribution, essential for ranking potential measurement locations from an exploration perspective. Next, we discuss approach estimating the belief distribution. To this end, DifFATD functions by executing a reverse diffusion process for a batch
{z(²)) } of size NB, where i e O, ....., Ng. guided by incremental set of observations (æ, ) as detailed in Algorithm[[] D. These observations are obtained through measurements collected at reverse diffusion steps 7, that satisfy
M, where M is measurement schedule. An element of this batch, (()) is referred to as particle. These particles implicitly form belief distribution over the entire search space z throughout reverse diffusion and are used to estimate uncertainty about æ. Concretely, we model the belief distribution simply as mixtures of NB isotropic Gaussians, with variance o²I.
(i) and mean # computed via Tweedie's operator T,
( (t) }) as follows:
E E((()
(1)
1
x
+ (1 a. (x
(3)
Var

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Algorithm Diffusion Dynamics Guided by Measurements
Require: T, Ng, So (ar 1r=0 (ār)T=o, I: f 0: {af ~N, () N(0, 1), fo
M, Qu 0
2: for to do
for: = 0 to NB do
1 <- T= = Vay x7 + -1-11 -a))()))) Where g(0) 4- so
I f- (1--1))) bi
Var-1ity z1() + +02
5:
-az
l-ar
I 2 (8)
v L0 || 1a. Il: lll, select elements of indexed by Qu.
Mesiurmmnt Guiddonee
7:
end for
8:
if
M then
t-
10:
Acquire new measurement at location ge and update: Q: + Qi-1 U St + 82-1 U (x]a
11:
end if
12:
end for
We assume that the reverse diffusion step T corresponds to the measurement step Utilizing the expression 3 we can express the belief distribution as follows:
Nu
p(zx|Qu E.-1)
Σ
a.N(
(4)
==
According to 28 the marginal entropy of this belief distribution can be estimated as follows:
NB
N ajexp
||
H(ielQr, 11-1 x
aglog
(5)
20
1=0
As per Eqn. uncovering the optimal measurement location (gt,) requires computing separate set of & for each possible choice of q:- Next, we present theorem that empowers to select the next measurement as the region with the highest total variance across (2 estimated from each particle in the batch conditioned on (Q,, #;1), effectively bypassing the need compute separate set of predicted search space et for each potential measurement location q:-
Theorem Assuming represents the set of possible measurement locations at step i, and that all particles have equal weights (o: = ajj Vi,j), then de is given by:
NB
Ne log
Eg -1a( 1g.
arg max VE
exp
20
where [t]g. selects element of indexed by qr-
We prove this result in Appendix. Its consequence is that the optimal choice for the next measurement location (q. (D lies the region of the measurement space where the predicted search space (o!") exhibits the greatest disagreement across the particles (i E O.... NB), quantified by metric, denoted as exp) score (qt), which enables ranking potential measurement locations to optimize explo-
ration efficiency. In cases where the measurement space consists of pixels, a.f() represents predicted estimates of the full image based on observed pixels ž,-1 so far.
expl
(ac)
20
We now delve into how DifJATD leverages the observations collected so to address exploitation effectively. To this end, DifAADD: (i) employs reward model (r&)) parameterized by ø. which is incre- mentally trained on supervised data obtained from measurements, enabling to predict whether spe- cific measurement location belongs the target of interest; (ii) estimates Ez, [log p( (ofte(C4 Qu, 1))
5

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step step
3
Conient wilhin
Shows high
particles
Bovere Diffusion peoces
Apply Twrrdie''
guided by measurements so far
Space
Exploratint
Explotarton!
X
PI
Consent withinn
Shows high
Ditlusion process
Apply Twaedie's Operstor estmatee Entire Search Space,
purticles and less
goided by messunements for
Reward under (0
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X
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4 Tu1
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under
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Apply Opentos to estimate Entire Search Space
Explonation
X
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Figure 2: An Overview of DiffATD.
representing the expected log-likelihood score at measurement location qt, denoted likeli*core (g:). as evaluating essential for prioritizing potential measurement locations from an exploitation standpoint. The following theorem establishes expression for computing likeliscore(g)
Theorem 2. The expected log-likelihood score at measurement location qu can be expressed:
(8) 4:
(i)
)2
likeli
(g()
exp
20
We present the derivation of Theorem 2 in the Appendix. likeli (qe) serves as a key factor in calculating the exploitation score measurement location 4t, where the exploitation score, exploit score (gr), is defined as the reward-weighted expected log- as shown below:
N
exploit score (qx) =
likeli soore
T (1 lac)
Expected lngliikllhood
According to Eqn. a measurement location is preferred for exploitation if it satisfies two conditions: (1) the predicted content at Gt. across the particles, highly likely to correspond to target of interest, determined by the reward model (rz) that predicts whether specific measurement
location belongs to the target; (2) the predicted content at qt, denoted as [+ Ig.- shows the highest degree of consensus among the particles, indicating that the content q: is highly predictable. Additionally, we demonstrate that maximizing the exploitation score synonymous with maximizing the expected reward at the current time step, highlighting that the exploitation score operates purely greedy strategy. We establish the relationship between exploit score (gt)) and a pure greedy strategy and present the proof in the Appendix.
Theorem 3. Maximizing exploit (gt) w.F. measurement location qe equiva- lent to maximizing expected reward as stated below: arg max4, lexploit Score ( arg maxg. Ex,-p(i (.. 1r
(g:))
is important to note that we randomly initialize the reward model parameters (ø) and update them progressively using binary cross-entie cross-entropy loss as new supervised data is acquired after each measurement. The training objective of reward model r's at measurement step t defined as below:
min
(y) log(ro((x)m))) + (1 - (()) log(1 - rl(()))
(8)

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Initially, the reward model is imperfect, making the exploitation score unreliable. However, this is not concern as DiffATD prioritizes exploration the early stages of the discovery process. Next, we integrate the components to derive the proposed DiffATD sampling strategy for efficient active target discovery. This involves ranking each potential measurement location ((t) time by considering both exploration and exploitation scores, as defined below:
(9) Here, xB)) function of the measurement budget that enables DiffATD achieve budget-aware balance between exploration and exploitation. After computing the scores (as defined in 9 for each measurement location gt. DiffATD selects the location with the highest score for sampling. The functional form of kc(5) is a design choice that depends on the specific problem. For instance, simple approach is to define k(B) as linear function of the budget, such as x(B3 = B-t We
Score(q.) x(B) expl=coree (9:) (1 x(B)) likeli
B4t"
empirically demonstrate that this simple choice of x(B) is highly effective across wide range of application domains, detail the DiffATD algorithm in and an overview in Figure
Algorithm DiffATD Algorithm
Require: T, Ng. s0, far ( (ārlr-o, M, Qu = 6,B
I: f == 0: { ~ ~N(00, 1) ~ N(O, 1), = 0. D. - 0, (k) = Set of All measurements, At =
(1)
2: for 7 to do
3: for to
NB do
4:
a (x(x+t) Viy x7
(0)
(a-aa))))) a-) Where 8(i so(x T)
'6)
oo. (1--))))1 Ir
Vār-10r
F--1
aoy
T-a
27
+ t
6:
a [|]== cV (1)'
[
[e.")
1q.11
7:
end for
M
then
9:
Compute expl expe (q:) and exploit (4:) using Equ. 6 and respectively for each qi l..
10:
Compute score(qe) using Eqn. 9 for each qe E & and sample a location with the highest score.
11:
+ 1, B (k) (k) q
12:
Update: Q1 + Q- Uqt H, < Øz-1 U [x]a
Update: D, + Di-1 U [x)ee (.)) R += g/
13:
Train with updated D, and optimize with
14:
end if
end
16:
Return R.
Experiments
Evaluation metries. Since ATD seeks to maximize the identification of measurement locations containing the target interest, we assess performance using the success (SR) of selecting mea- surement locations that belong to the target during exploration in partially observable environments. Therefore, SR defined as:
SR
(a), L number of tasks.
(10)
L min (B, U.)
Here, Us denotes the maximum number of measurement locations containing the target in the i-th search task. We evaluate DiffATD and the baselines across different measurement budgets E {150, 200, 250, 300) for various target categories and application domains, spanning from medical imaging to remote sensing. Our code and models publicly available at this link
Baselines. We compare our proposed DiffATD policy to the following basclines:
Random Search (RS), which unexplored measurement locations are selected uniformly at random.
Max-Ent approach ranks a set of unexplored measurement locations based on expl (q:) and then selects 4: corresponding to the maximum value of (core (qt).
Greedy-Adaptive (GA) approach ranks a set of unexplored measurement locations based on exploit score and then selects di corresponding to the maximum value of exploit score (core( (4)) Like
DiffATD, GA approach updates (ra) using Equation after each observation.
7

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Active Discovery of Objects from Overhead Imagery We begin the evaluation by comparing the performance of DiffATD with the baselines in terms SR. For this comparison, we consider various targets (e.g., truck, plane) from the DOTA dataset [29] and present the results in Table The empirical outcome indicates that DiffATD significantly outperforms all baselines, with improvements ranging from 7.01 % to 17.23% % over the most competitive method across all measurement budgets. We also present visualizations
DiffATD's exploration strategy in Fig. 3 demonstrating its effectiveness in ATD. As depicted in Fig. B DiffATD efficiently explores the search space, uncovering distinct target clusters within the measurement budget, highlighting its effectiveness in balancing exploration and exploitation. Similar visualizations with different target categories in the Appendix.
Discovered Target Discovered Ta Targer by DIEATTD by Maxe Ent
Discovered Target by DiFFATD
Discovered Target by Mane East
Table I: SR Comparison with Baseline Approaches
Active Discovery with targets, e.g., plane, truck
Method
= 200
= 250
= 300
Sampled Region
Sampled Region by Max Ens
Sampled Region by DiEEATD
Sampled Region by Max Ens
by DiIATTD
RS
0.1990
0.2487
0.2919
Max-En
0,4625
0,5524
0.6091
GA
0,4586
0.5961
0.6550
DiffATD
0.5422
0.6379
0.7309
Figure 3: Active Discovery of Plane, Playground.
Active Discovery of Species Next, evaluate the efficacy of DifAATD in uncovering unknown species from iNaturalist [30. The target species distribution is formed by dividing a large geospatial region into equal-sized grids and counting target species occurrences
each grid, detailed in Appendix. We compare DifAATD with the baselines in terms of SR, and across varying B. The results are presented in Table 2 We observe significant improvements in the performance of the proposed DisJATD approach compared to all baselines in each measurement budget setting, ranging from 8.48% % to 13.86% % improvement relative to the most competitive method. In Fig. we present qualitative comparison of the exploration strategies of DiffATD and GA, illustrating that DiffATD uncovers more target clusters compared the GA approach within fixed sampling budget. DIBATD
Table 2: SR Comparison with Baseline Approaches
Active Discovery of Coccinella Septempunctata
Method
100
150
200
RS
0.1241
0.1371
0.1932
Max-Ent
0,4110
0.5044
0.5589
GA
0.4345
0.5284
0.5826
DifJATD 0.4947
0.5732
0.6401
Figure 4: ATD of Species (purple targets).
Active Discovery of Skin Disease Next, we test the impact of DiffATD in the medical imaging setting. To this end, compare the performance of DiffATD with the baselines terms of SR using target classes from the skin imaging dataset [31]. We compare the performance across varying measurement budgets The results are presented in Table 3 We observe significant improvements in the performance of the proposed DiffAT1) approach compared all baselines in each measurement budget setting, ranging from 7.92% to 10.18% improvement relative to the most competitive method. In Fig. 5 present qualitative comparison of the exploration strategies of DiffATD and Max-Ent. As shown in Fig. 5 DiffATD efficiently explores the search space, uncovering two distinct target clusters within the measurement budget, highlighting its effectiveness in balancing exploration and exploitation. Several such visualizations and the results with other datasets are in Appendix.
Discoveree Target Discovered Target
Discoweeed Target Discowered Target Ent
by DIEAATD
Max:
DURATTD
Table SR Comparison with Baselines.
Active Discovery of Malignant Skin Discases
S Sumpled Region DIEIATD
Sampled Region by Max Eatt
Sampled Region DIELATD
Sampled Region Mas
Method
150
200
250
RS
0.2777
0.2661
0.2695
Max-Ent
0,5981
0,5816
0,5717
GA
0.8396
0.8261
0.7943
DiffATD
0.9061
0.8974
0.8752
Figure 5: Active Discovery of Skin Disease.
8

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Active Discovery of Bone Suppression Next, we evaluate DiffADD on the Chest X-Ray dataset [32. with results shown in Table The findings follow a similar trend to previous datasets, with DiffATD achieving notable performance improvements of 41.08% % to 59.22% across all measurement budgets. These empirical outcomes further reinforce the efficacy of DiffATI in active target discovery. Visualizations of DiffATD's exploration strategy are provided in Fig. 6 with additional examples are presented in the Appendix.
Discovered Targees Discovernd Targets
Discowened Targuts by DIIIA
Discovered Torgets
by DIITATD by Mixs-
by Max- Ent
Table 4: SR Comparison with Chest X-Ray Dataset
Active Discovery of Bone Suppression
Method
200
250
300
Sumpled Regiun
Sumpleal Region by Mare
Sampled Region by DERATD
Sampled Region
by DIRAATI
by Mas Ent
RS
0. 0.1925
0,2501
0.2936
Max-Ent
0. 0.1643
0.2194
0.2616
GA
0. 0.1607
0.2010
0.2211
DiffATD
0.3065
0.3733
0.4142
Figure 6: Active Discovery of Bone Suppression.
Qualitative Comparison with GA Approach with that of Greedy-Adaptive (GA) using
We compare the exploration strategy of DiffATD
CelebA samples, as shown in Fig. 7 DiffATI achieves better balance between exploration and exploitation, leading to higher success rates and more efficient target discovery within fixed budget. In contrast, GA focuses solely on ex- ploitation, relying on an incrementally learned reward model rd. These visual comparisons highlight the limitations of purely greedy ap- proaches, such as GA, especially when targets have complex or irregular structures with spa- tially isolated regions. GA often struggles early Figure 7: Active Discovery of Eye, hair, nose, lip. in the search, when training samples are limited, the reward model tends to overfit noise, mis- guiding the discovery process. In contrast, DiffATD minimizes early reliance on reward-based exploitation, gradually increasing it as more measurements are collected and the reward model strengthens. This adaptive process makes DiffATD more resilient and reliable than GA. More qualitative results are in the Appendix.
Discovered Target
Discovered Target
Discovered Target DiRAAD
Diseavened Target
GA
Sampled Region by DillAD
Sampled Region by GA
Sampled Nogion by DifFATD
Sampled Region by GA
Effect of x(B) We conduct experiments to assess the impact of k(B) on DiffATD's active discovery performance. Specifically, we investigate how amplifying the exploration weight, by setting x(B)
{0, x((x B with >> 1, and
Table 5: Effect of k(B)
enhancing the exploitation weight by setting a < 1, influ- ence the overall effectiveness of the approach. We present results for a E datasets, as shown in Table The best performance is achieved with a = 1, and the results suggest that extreme values of (either too low too high) hinder perfor- mance, as both exploration and exploitation are equally crucial to achieve superior performance.
Performance across varying o with B 200
using the DOTA and Skin
Datnset
0.2
1.0
5.0
DOTA Skin
0.5052 0.8465
0.5422 0,8974
0.4823
0.8782
Comparison with Supervised and Fully Observable Approach To evaluate the efficacy of the proposed DiffATD framework, we compare its performance to fully supervised SOTA semantic segmentation approach, SAM [33), that operates under full observability of the search space, referred as FulISEG. Note that during inference, FullSEG selects the top B most probable target regions for measurement in shot manner. We present the result for diverse target categories with = 300 in Table We observe that DifFATD outperforms SAM for rare targets, such skin diseases, while performing comparably to FulISEG for non-rare targets like vehicles, planes, etc., despite never observing the full search area and being trained entirely in an unsupervised manner, unlike FulISEG. This further showcases the strength of DiffATD in active target discovery in a partially observable environment.
Active Discovery of Targets
Method Skin
DOTA
FulISEG 0.6221
0.8731
DifJATD 0.8642
0.7309
Table SR Comparison.

---

Exploration Scure (cagl==0) Mussuremen Space
Likeliood Score (likd)--))) Across Meaouremnnt Space
Confalence ofty Acmus Measurement Space
Mearermment
Ranked by DiNATT
Playgoound Turger
Initial step
Ground Truth Mask
Exploration Scoce (exp)eing
likelhood Scoce (Exeljemn) Acnoss Measunemem Space
Confidence Score of Accoss Moasssement Spacor
Measuremeent Location Ranked by DiElATD
Acrosa Measurement Space
Final step
Figure 8: Explamation of DiffATD. Brighter indicates higher value.
Visualizing DiffATD's Exploration Behavior Different Stage We illustrate the behavior of DiffATD with an example. As shown in Fig. g during the initial search phase, DiffATD prioritizes the exploration score when ranking measurement locations. However, the search nears its final stages, rankings are increasingly driven by the exploitation score, as defined Eqn. 7 As the search progresses, the confidence of re and likelisore(() (.) become more accurate, making the exploit Shore (.) more reliable, which justifies DiffATD's increasing reliance on in the later phase. More such visualizations are presented in the Appendix.
Comparison With Vision-Langune LanguaeL Model We conduct comparisons between DifTATD and two State-of-the-art VLMs: GPT-4o and Gemini, on the DOTA dataset. The corresponding empirical results are summarized in the following Table We observe that DiffATD consistently outperforms VLM baselines across different measurement budgets. These findings underscore DifFATD's ad advantage over alternatives like VLMs in the ATD setting, driven by its principled balance of exploration and exploitation based on the maximum entropy framework. Additionally, in Figure D we present comparative exploration strategies for different targets from DOTA provide further intuition.
Ground Truth Mask
Sampled Mask DiffATD
Sampled Mask Gemini
Sampled Mask GPT-40
Table 7: Quantitative Comparison with VLM using DOTA Overhead Imagery Dataset
Active Discovery with targets, e.g., plane, truck
Method
150
B 180
B 300
Ground Truth Mask
Sampled Mask by DifEATD
Sampled Mask by Gemini
Sampled Mask by GPT-44 o
GPT4-o 0.3383
0.3949
0.5678
Gemini
0.4027
0.4608
0.6453
DifFATD
0.4537
0.5092
0.7309
Figure 9: Active Discovery of Plane, Truck.
Conclusions
We present biffusion-guider Active Target Discovery (DiffATD), novel approach that harnesses diffusion dynamics for efficient target discovery in partially observable environments within fixed sampling budget. DiffATD eliminates the need for supervised training, addressing key limitation of prior approaches. Additionally, DifJADD offers interpretability, contrast to existing black-bor policies. Our extensive experiments across diverse domains demonstrate its efficacy. We believe our work will inspire further exploration of this impactful problem and encourage adoption of DiffATD in real-world applications across diverse fields.
10

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This research was partially supported by the National Science Foundation (CCF-2403758, IIS-2214141), Army Research Office (W911NF2510059), Office of Naval Research (N000142412663), Amazon.
Ackmowledgement
References
[1] Dinesh Jayaraman and Kristen Grauman. Look-ahead before you leap: end-to-end active recognition by forecasting the effect of motion. In Computer Vision-ECCV200 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part V 14, pages 489-505. Springer, 2016.
[2] Dinesh Jayaraman and Kristen Grauman. Learning to look around: Intelligently exploring unseen environments for unknown tasks. In Proceedings of the IEFE conference on computer vision and pattern recognition, pages 1238-1247, 2018.
[3] Bo Xiong and Kristen Grauman. Snap angle prediction for 360 panoramas. In Proceedings of the European Conference Computer Vision (ECCV), pages 3-18, 2018.
[4] Iris Huijben, Bastiaan S Veeling, and Ruud JG Sloun. Deep probabilistic subsampling for task-adaptive compressed sensing. In 8th International Conference on Learning Representations, ICLR 2020, 2020.
[5] Cagla D Bahadir, Alan Q Wang, Adrian V Dalca, and Mert R Sabuncu. Deep-learning optimization of the under-sampling pattern in mri. IEEE Transactions Computational Imaging, 6: 139-1152 1552, 2020.
[6] Hans Van Gorp, Iris Huijben, Bastiaan Veeling, Nicola Pezzotti, and Ruud JG Van Sloun. Active deep probabilistic subsampling. In International Conference Machine Learning. pages 10519- PMLR, 2021.
[7] Tim Bakker, Herke van Hoof, and Max Welling. Experimental design for mri by greedy policy search. Advances in Neural Information Processing Systems, 33: 18954-18966, 2020.
[8] Tianwei Yin. Zihui Wu, He Sun, Adrian V Dalca, Yisong Yue, and Katherine L Bouman. End-to-end sequential sampling and reconstruction for mri. arXiv preprint arXiv: 200. 064606 2021.
[9] Tristan SW Stevens, Nishith Chennakeshava, Frederik J de Bruijn, Martin Pekař, and Ruud JG van Sloun. Accelerated intravascular ultrasound imaging using deep reinforcement learning. In ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2216-1220 IEEE, 2022.
[10] Thomas Sanchez, Igor Krawezuk, Zhaodong Sun, and Volkan Cevher. Closed loop deep bayesian inversion: Uncertainty driven acquisition for fast mri. 2020.
[11] Oisin Nolan, Tristan SW Stevens, Wessel L van Nierop, and Ruud JG van Sloun. Active diffusion subsampling. arXiv preprint 2tt.:2400.113888. 2024.
[12] Burak Uzkent and Stefano Ermon. Learning when and where to zoom with deep reinforce- ment learning. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pages 12345-12354, 2020.
[13] Anindya Sarkar, Michael Lanier, Scott Alfeld, Jiarui Feng, Roman Garnett, Nathan Jacobs, and Yevgeniy Vorobeychik. A visual active search framework for geospatial exploration. In Proceedings of the IÉEE/CVF Winter Conference on Applications of Computer Vision, pages 8316-8325, 2024.
[14] Anindya Sarkar, Nathan Jacobs, and Yevgeniy Vorobeychik. A partially-supervised reinforce- ment learning framework for visual active search. Advances in Neural Information Processing Systems, 36: 36:12245-111 12270, 2023.
[15] Quan Nguyen, Anindya Sarkar, and Roman Garnett. Amortized nonmyopic active search via deep imitation learning. arXiv preprint 1031, 2024.
11

---

[16] Roman Garnett, Yamuna Krishnamurthy, Xuehan Xiong, Jeff Schneider, and Richard Mann. Bayesian optimal active search and surveying. arXiv preprint vrXiv:1206.6400 2012.
[17] Shali Jiang, Gustavo Malkomes, Geoff Converse, Alyssa Shofner, Benjamin Moseley, and Roman Garnett. Efficient nonmyopic active search. In International Conference on Machine Learning, pages 1714-1723. PMLR, 2017.
[18) Shali Jiang, Roman Garnett, and Benjamin Moseley. Cost effective active search. Advances in Neural Information Processing Systems, 32, 2019.
[19] Samrudhdhi B Rangrej, Chetan L Srinidhi, and James J Clark. Consistency driven sequential transformers attention model for partially observable scenes, arXiv preprint vrXiv:224.006666 2022.
[20] Aleksis Pirinen, Anton Samuelsson, John Backsund, and Kalle Aström. Aerial view goal localization with reinforcement learning. arXiv preprint Siti::2209.06994 2022.
[21] Anindya Sarkar, Srikumar Sastry, Aleksis Pirinen, Chongjie Zhang, Nathan Jacobs, and Yev- geniy Vorobeychik. Gomaa-geo: Goal modality agnostic active geo-localization. arXiv preprint arXiv:2406.0199 2024.
[22] Yang Song, Jascha Sohl-Dicksten Dicksteii, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-hased generative modeling through stochastic differential equations. arXiv preprint arXiv:201 13456, 2020.
[23] Brian DO Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12(3):313332, 1982.
[24] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances neural information processing systems, 33:6840-6851, 2020.
[25] Hyungjin Chung, Jeongsol Kim, Michael T Mccann, Mare L Klasky, and Jong Chul Ye. Diffu- sion posterior sampling for general noisy inverse problems. arXiv preprint arXiv:2209. 14687, 2022.
[26] Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guum guided diffusion models for inverse problems. In International Conference on Learning Representations, 2023.
[27] Litu Rout, Negin Raoof, Giannis Daras, Constantine Caramanis, Alex Dimakis, and Sanjay Shakkottai. Solving linear inverse problems provably via posterior sampling with latent diffusion models. Advances in Neural Information Processing Systems, 36, 2024.
provably
[28] John R Hershey and Peder A Olsen. Approximating the kullback leibler divergence between gaussian mixture models. 2007 IEEE International Conference on Acoustics, Speech and Signal Processing-(CASSSP00 volume 4, pages IV-317. IEEE, 2007.
(29) Gui-Song Xia, Xiang Bai, Jian Ding, Zhen Zhu, Serge Belongie, Jiebo Luo, Mihai Datcu, Marcello Pelillo, and Liangpei Zhang. Dota: A large-scale dataset for object detection in aerial images. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3974-3983, 2018.
[30] iNaturalist. https://www.inauuraise
[31] Veronica Rotemberg, Nicholas Kurtansky, Brigid Betz-Stablein, Liam Caffery, Emmanouil Chousakos, Noel Codella, Marc Combalia, Stephen Dusza, Pascale Guitera, David Gutman, et al. A patient-centric dataset of images and metadata for identifying melanomas using clinical context. Scientific data, 8(1):34, 2021.
[32] Bram Van Ginneken, Mikkel B Stegmano, and Marco Loog. Segmentation of anatomical structures in chest radiographs using supervised methods: comparative study on public database. Medical image analysis, 10(1):19-40, 2006.
12

---

[33] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitchead, Alexander Berg, Wan Yen Lo, al. Segment anything. In Proceedings of the IEEF/CVF International Conference Computer Vision, pages 4015-4026, 2023.
[34] Cheng-Haa Han Lee, Ziwei Liu, Lingyun Wu, and Ping Luo. Maskgan: Towards diverse and interactive facial image manipulation. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pages 5549,,558, 2020.
[35] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arX1v:20100002502, 2020.
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Appendix: Online Feedback Efficient Active Target Discovery in Partially Observable Environments
Overview of the Contents
A: Proofs of Theoretical Results
22
A.1 Proof Proposition
22
A.2 Proof of Theorem 1
22-23
A.3 Proof of Theorem 2
23-24
A.4 Proof of Theorem 3
23
B: Empirical Analysis of Active Target Discovery across Diverse Domains
24
B.1 Active Target Discovery of Different Parts of Human Face
24
B.3 Active Target Discovery of Handwritten Digits
25
C: Qualitative Comparisons with Greedy Adaptive Approach
25
C.I Qualitative Comparisons using Lung Disease, Skin Disease, DOTA, CelebA Images
25-27
D: Additional Visualization of Exploration Strategy of DifTATD
27
D.I Comparative Visualizations using Lung Disease, Skin Disease, DOTA, CelebA
27-29
Images
E: Details of Training and Inference
30
E.I Details of Computing Resources, Training, and Inference Hyperparameters
30
E.2 Details of Reward Model r
30
F: Challenges in Active Target Discovery for Rare Categories
30 -31
G: Scalability DiffATD on Larger Search Spaces
H: Additional Results Access the Effect of x(33)
Rationale Behind Uniform Measurement Schedule Over the Number of Reverse Diffusion Steps
31-32
J: Performance of DifFATD Under Noisy Observations
32
K: Species Distribution Modelling Active Target Discovery Problem
33
L: Statitical Significance Results of DiSTATD
33
M: Comparison With Multi-Armed Bandit Based Method
33-34
N: Segmentation and Active Target Discovery are Fundamentally Differrnt Task
34
O: More Details on Computational Cost across Search Space
34
P: More Visualizations on DifrATD's Exploration vs Exploitation strategy at Different
34-37
Stage
Q: Importance of Utilizing a Strong Prior in Tackling Active Target Discovery
37
R: Limitations and Future Work
37
S: Notation Table
37-38
21

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A
Proof of Theoretical Results
A.1
Proof of Proposition
Proof.
arg max ( x Qu, it-1 41 [x. [lo Qt, log Ft
9:
arg max 9t
arg max Vt
His (t,
H x. Si-))
remains independent of the qu Therefore, this term con disregarded when optimizing for Qr
arg max [H (ē; Qc (e-))
A.2 Proof of Theorem
Proof. We demonstrate that maximizing the marginal entropy of the belief distribution defined in Equation does require computing separate set of particles for every possible choice of measurement location when the action corresponds to selecting measurement location. Since the measurement locations Q: = Qt- U q only differ in the newly selected indices q within the
arg max, the elements of each particle (#) remain unchanged across all possible Qt, except at the indices specified by d: Exploiting this structure, we decompose the squared L2 norm into two parts: one over the indices in and the other over those in Q:-1- 1- The term associated with Q--1 becomes constant in the arg max and can disregarded. Consequently, the formulation reduces the computing of the squared L2 norms exclusively for the elements corresponding to We denote as the set of we can write,
possible measurement locations at step f. Utilizing Equation
NB
NB
||
exp 9t
ag
ajexp
20
1=0
||0
x 21)) 112
4t
exp
arg max
log
cxp
20
(By assuming, a; Ojj Vi,j)
Eneq, (10 Ja 100 [a)2
4t
arg max
log
exp
4t
20
-16661 12 Ereq.
(10(1)) (06 1r)2
4:
cxp
arg
log
exp
20
(1 19.
[0 lge)
((a(0)) |r [80 1.)
exp
arg max
log
II exp
II exp
20
20
E
rEQu-1
(10 (1)
[1] [g.) )2
(La
(10
cup X arg max
+
Σ rEQ...
202
20
ignore doem't 't elepnnd the choice
22

---

([
[ lq )2
d:
arg max
2
DEER
NB
NB
E EgEEk (11
(8)
[1c] 10: )
4:
exp
arg max
log
11
20
f=0
A.3 Proof of Theorem 3
pure greedy strategy selects the measurement location that maximizes the expected reward at the current time step, as defined below:
arg max E BB: v)br
ge
/
arg max
l(ge)
In order to maximize I(q:) w.r.t qt. do the following:
V (1:) arg max
St di:
arg max ge
1e. 2.1) log p(2, Qu 32 121 d8;
We obtain the last equality using the following identity:
(=(x) Vo log (o V (x)
We simplify the expression using the definition of expectation, as shown below:
arg max 4s
qo log pl Qu, T
r (Gdlee
Maximizing expected log likelikooloo score, ie., likeli (.). Reward at current time.
By definition, it is equivalent the following
arg max |exploit score (g:)
(as defined in Equation 7
A.4 Proof of Theorem 2
Proof. We start with the definition of entropy H:
Ez, p(. Q2, T. -,-1)] = H(. T
Substituting the expression of (0, Qt, 11) as defined in Equation we obtain:
5
and by setting aa =
NB
Ne
|
E,, log 2,11
log
exp
20
1=0
1=0
Eneq. (12
Es, [log p(tz/Qr, 8. x Σ log
exp
20
23

---

Assuming & is the set of potential measurement locations at time step I, and Q2 = Qi-1 U ge. where
q: E k.
Emnexalaf - -10 la.) 12+
( 110 1.
Es, (ogg((()000 --
log
exp
20
i.j
(litt
(1)
(f)
1n
(10
[ 1o)
Es, (etlloo(elQQ,
Σ log II
exp
191
II exp
20
20
Pe
rEQu-1
([at
)2
(La)
Ex, log (( x
19
20
20
P
rEQ
Next, we compute the expected log-likelihool at specified measurement location q.. Accordingly, ignore all the terms that do not depend q:- This simple observation helps us simplify the above expression as follows:
Egg (loog((s.)Qu. (r,
Σ 2
(1
(2) .9
()) [
19.
)2
20
qt
expected log. Likelilond measurement qr
Equivalently, we can write the above expression as:
NR N
(0)
[+t
1ge)
Eg, log p(;, 8
exp
W
20
91
i=0
1=
likelpooro(q)) (gc)
By definition, the I.H.S of the above expression is the same as likeliscore (ge).
B Empirical Analysis of Active Target Discovery across Diverse Domains
B.1 Active Discovery of Different Parts of Human Face
We compare DiffATD with the baselines with the human face as the target from the CelebA dataset 34 and report the findings in Table 8 These results reveal similar trend to that observed with the previous datasets. We observe significant performance gains with DifAAT over baselines, with improvements of 42.60% to 60.79% across all measurement budgets, demonstrating its mastery in balaneing exploration and exploitation for effective active target discovery. We present visualizations of DiffATD's s exploration strategy in Fig I0 with additional visualizations are in appendix D
Discovened Discovered by
Diecovered Torpet
Discovered Target by Mas-
by DiEATT
Table 8: SR Comparison with CelebA Dataset
Active Discovery with as target
Method
200
250
300
Sampled Region
Sumplee Sampled Region
Sampled
TD
RS
0.1938
0.2441
0.2953
Max-Ent
0,2399
0.3510
0.4498
GA
0,2839
0.3516
0.4294
DiffATD
0.4565
0.5646
0.6414
Figure 10: Active Discovery of regions with Face.

---

B.2 Active Discovery of Hand-written Digits
Here, we evaluate performance by comparing DiffATD with the baselines using the SR metric. We compare the performance across varying measurement budgets B. The results are presented in Table We observe significant improvements in the performance of the proposed DifJATD approach compared to all baselines in each measurement budget setting, ranging from 16.30% to 45.23% improvement relative to the most competitive method. These empirical results are consistent with those from other datasets explored, such as DOTA, and CelebA. We present a qualitative comparison of the exploration strategies of DiffATD and Max-Ent through visual illustration. As shown in Fig. DiffATD efficiently explores the search space, identifying the underlying true handwritten digit within the measurement budget, highlighting its effectiveness in balancing exploration and exploitation. We provide several such visualizations in the following section.
Table 9: SR comparison with MNIST Dataset
Active Discovery of Handwritten Digits
Method
100
B 150
200
RS
0.1270
0.1518
0.1943
Max-Ent
0.5043
0.6285
0.8325
GA
0.0922
0,4133
0,5820
DiffATD
0.7324
0.8447
0.9682
Discovered Target Discovered Target
Discovered Target by DifFATD
Discovered Target by Max-Ent
by DifFATD
by Max-Ent
S Sampled Region by DifFATD
Sampled Region by Max-Ent
Sampled Region by DifFATD
Sampled Region by Max-Ent
4
Figure 11: Visualization of Active Discovery of Handwritten Digits.
C Qualitative Comparison with Greedy Adaptive Approach
C.1 Qualitative Comparisons using Lung Disease, Skin Disease, DOTA, and CelebA Images
In this section, we present additional comparative visualizations of DiffATD's exploration strategy against Greedy-Adaptive (GA), using samples from diverse datasets, including DOTA. CelebA and Lung images. These visualizations are shown in Figures 13
14 15 In each case, DiffATD strikes strategic balance between exploration and exploitation, leading to a notably higher success rate and more efficient target discovery within fixed budget, compared to the greedy strategy, which focuses solely on exploitation based on an incrementally learned reward model rs. These qualitative observations emphasize key challenges in the active target discovery problem that are difficult to address with entirely greedy strategies like GA. For instance, the greedy approach struggles when the target has a complex and irregular structure with spatially isolated regions. Due to its nature, once identifies a target one region, begins exploiting neighboring areas, guided by the reward model that assigns higher scores to similar regions. As result, such methods struggle
25

---

to discover spatially disjoint targets, shown in these visualizations. Interestingly, the greedy approach also falters noisy measurement environments due its over-reliance on the reward model. Early in the search process, when training samples are limited, the model tends to overfit the noise, misguiding the discovery process. In contrast, our approach minimizes reliance on reward-based exploitation in the early stages. As more measurements are collected, and the reward model becomes incrementally more robust, our method begins to leverage reward-driven exploitation more effectively, This gradual adaptation makes our approach significantly more resilient and reliable, particularly in noisy environments, compared to the greedy strategy.
Discovered Target Discovered Target by DifTATD
Discovered Target Discovered Target by DifFATD
by GA
by GA
Sampled Region by DifFATD
Sampled Region by GA
Sampled Region by DifFATD
Sampled Region by GA
Figure 12: Visualization of Active Discovery of Lung Disease.
Discovered Target Discovered Target by DifFATD
Discovered Target by DiffATD
Discovered Target by GA
by GA
Sampled Region by DiffATD
Sampled Region by GA
Sampled Region by DifFATD
Sampled Region
by GA
Figure 13: Visualization of Active Discovery of (left) Truck and (right) Plane
26

---

Discovered Target Discovered Target by DiffATD
Discovered Target by DiffATD
Discovered Target by GA
by GA
Sampled Region by DD
Sampled Region by GA
Sampled Region by DiffATD
Sampled Region by GA
Figure 14: Visualization of Active Discovery of Eye, hair, nose, and lip.
Discovered Target Discovered Target by DifFATD by GA
Discovered Target Discovered Target by DifFATD
by GA
Sampled Region by DifFATD
Sampled Region by GA
Sampled Region by DiffATD
Sampled Region
by GA
Figure 15: Visualization of Active Discovery of Skin Disease.
D
Additional Visualizations of the Exploration Strategy of DifFATD
D.1
Comparative Visualizations using Lung Disease, Skin Disease, DOTA, CelebA Images
In this section, we provide further comparative visualizations of DiffATD's exploration strategy versus Max-Emi using samples from a variety datasets, including DOTA, CelebA, Skin, and Lung images. In each example, DiffATD demonstrates a strategic balance between exploration and exploitation resulting a significantly higher success rate and more effective target discovery within predefined budget compared to strategies focused solely on maximizing information gain. These visualizations further reinforce the effectiveness of DiffATD in active target discovery within partially observable environments.
We present the visualization in figures 16
17
18
19
20
21
27

---

Discovered Target Discovered Target by DifFATD
Discovered Target by DiffATD
Discovered Tar Target by Max-Ent
by Max-Ent
Sampled Region by DiffATD
Sampled Region by Max-EMi Ent
Sampled Region by DifFATD
Sampled Region by Max-En
E
Figure 16: Visualizations of Active Discovery of (Ieft) large-vehicle, and (right) Plane.
Discovered Target Discovered Target Discovered Target by DifEATD
Discovered Target
by Max-Ent
by DifFATD
by Max-Ent
Sampled Region by DifFATD
Sampled Region by Max-Ent
Sampled Region by DifFATD
Sampled Region
by Max-Ent
Figure 17: Visualizations of Active Discovery of (left) Skin disease, and (right) Plane.
Discovered Target Discovered Target by DiffATD
Discovered Target Discovered Target
by Max-Ent
by DifFATD
by Max-Ent
Sampled Region by DiffATD
Sampled Region by Max-Em
Sampled Region by DifFATD
Sampled Region by Max- Max-Ent
Figure 18: Visualizations of Active Discovery of (left) human face, and (right) lung disease, such
28

---

Discovered Target Discovered Target
Discovered Target Discovered Target by DifIATD
by DiffATD
by Max-Ent
by Max-Em Ent
Sampled Region by DifFATD
Sampled Region by Max-Ent
Sampled Region by DiffATD
Sampled Region
by Max-Ent
Figure 19: Visualization of Active Discovery of Lung Disease.
Discovered Target Discovered Target by DiffATD
Discovered Target Discovered Target by DifFATD
by Max-Ent
by Max-Ent
Sampled Region by DD
Sampled Region by Max-Ent
Sampled Region by DifFATD
Sampled Region by Max-Ent
Figure 20: Visualization of Active Discovery of hair, eye, nose, and lip.
Discovered Target Discovered Target by DifFATD
Discovered Target by DiffATD
Discovered Target by Max-Ent
by Max-Emi Ent
Sampled Region by DifFATD
Sampled Region by Max-Max-ii -Ent
Sampled Region by DifFATD
Sampled Region by Max-Ent
Figure 21: Viz. of Active Discovery of Lung Disease (right) and hair, eye, nose, and lip (left).
29

---

E Details of Training and Inference
E.1 Details of Computing Resourees, Training, and Inference Hyperparameters
This section provides the training and inference hyperparameters for each dataset used in experiments. We use DDIM [35] as the diffusion model across datasets. The diffusion models used in different experiments dataset, we use 32-dimensional diffusion time-step embeddings, with the diffusion model consisting of 2 residual blocks. We select the time-step embedding vector dimension to match the input feature size, ensuring the diffusion model can process it efficiently. The block widths are set to [32, 64, 128), and training involves 30 diffusion steps. DOTA, CelebA, and Skin imaging datasets share the same input feature size of [128, 128,3) 3] and architecture, featuring 128-dimensional time-step embeddings and a diffusion model with 2 residual blocks of width [64, 128, 256, 256, 512]. For these datasets, we perform training with 100 diffusion steps. We use 128-dimensional time-step embeddings for the Bone dataset and a diffusion model with 2 residual blocks (each block width: [64, 128, 256, 2561). We use 100 diffusion steps during training. We set the learning rate and weight decay factor to le 14 for all experimental settings. We set measurement schedule (M) of 100 for measurement budget (B) of 200, ensuring that B z M' where T is the total number of reverse diffusion steps, set to approximately 2000 for the DOTA, CelebA, and Skin datasets. Finally, all experiments are implemented in Tensorflow and conducted on NVIDIA A100 40G GPUs. Our training and inference code will be made public.
based on widely adopted U-Net-style architecture. For the MNIST
T
E.2 Details of Reward Model Te
Our proposed method, DifFATD, utilizes a parameterized reward model, To. steer the exploitation process. To this end, we employ a neural network consisting of two fully connected layers, with non-linear ReL.U activations as the reward model (ræ). The reward model's goal is to predict score ranging from 0 to 1, where a higher score indicates a higher likelihood that the measurement location corresponds the target, based on its semantic features. Note that the size of the input semantic feature map for a given measurement location can vary depending on the downstream task. For instance, when working with the MNIST dataset, we use a x 1 pixel the input feature, while for other datasets like CelebA, DOTA, Bone, and Skin imaging, we use an 4 x 4 patch as the input feature size. After each measurement step, we update the model parameters (σ) using the objective function outlined in Equation 8 Additionally, the training dataset is updated with the newly observed data point, refining the model's 's predictions over time. Naturally, as the search advances, the reward model refines its predictions, accurately identifying target-rich regions, which makes it progressively more dependable for informed decision-making. The reward model architecture is consistent across datasets, including Chest X-ray, Skin, CelebA, and DOTA. It consists of 1 convolutional layer with a 3 x 3 kernel, followed by 5 fully connected (FC) layers, each with its own weights and biases. The first FC layer maps an input of size (input eize)? ? to output of size 4 with weights and biases of size
eise)) 4 and [4] respectively. The second FC layer transforms an input of dimension 4 to an output of size 32 with a 2-dimensional weight of size [4, (4,32] and a bias of size [32]. The third FC layer maps 32 inputs to 16 outputs via weight matrix of shape [32, 16) and bias vector of size [16]. The pre-final FC layer transforms inputs of size 16 to outputs of size 8 with [16, 8] weights, and a bias of shape [8]. The final FC layer produces output of size 2, with weights of size [8, 2] and a bias of size [2]. representing the target and non-target scores. The reward model uses the leaky ReLU activation function after each layer. We update the reward model parameters after each measurement step based on the objective in Equation [8 The reward model is trained incrementally for 3 epochs after each measurement step using the gathered supervised dataset resulting from sequential observation, with a learning rate of 0.01.
F
Challenges in Active Target Discovery for Rare Categories
To highlight the challenges in Active Target Discovery for rare categories, such as skin disease, we conduct an experiment comparing the performance of DiffATD with a fully supervised -tate-of-the-art semantic segmentation model, SAM, which operates under full observability of the search space (referred to as FullSEG). During inference, FullSEG selects the top B most probable target regions for measurement in a single pass. We present the results for Skin Disease the target, with varying
30

---

Table 10: Comparison with supervised and fully observable method
Active Discovery of Targets on Skin Images
Method
B = 150
B = 200
B = 250
FulISEG
0.7304
0.6623 0.8974
0.6146
DifIATD
0.9061
0.8752
budgets B, in Table 10 A significant performance gap is observed across different measurement budgets. These results underscore the challenges in Active Target Discovery for rare categories, as state-of-the-art segmentation models like SAM struggle to efficiently discover rare targets, like skin disease, further demonstrating the effectiveness of DiffATD.
G Scalability of DifTATD on Larger Search Spaces
To empirically validate DiffATD, we conduct experiments across diverse domains, including remote sensing (DOTA) and medical imaging (Lung Disease dataset), and explore targets of varying com- plexity, from structured MNIST digits to spatially disjoint human face parts. These cases require strategic exploration, highlighting DifTATD's adaptability. To assess scalability, we compare DifFATD and the baseline approaches with a larger search space size of 256 256, and present the result in Our findings reinforce DifTATD's effectivvness in complex tasks.
Table II
Table 11: Results With Larger Search Space (256 256) using DOTA Dataset
Active Discovery of Objects, e.g. Plane, Truck, etc.
Method
B = 100
B 150
B 200
RS
0.1990
0.2487
0.2919
Max-En
0.3909
0.4666
0.5759
GA
0.4780
0.5632
0.6070
DiffATD
0.5251
0.6106
0.7576
H
Additional Results to Access the Effect of s((3)
In the main paper, we analyze how the exploration-explooiaaion tradeoff function impacts search per- formance, using both the DOTA and Skin imaging datasets (see Table 12 for the result). Additionally, in this section, we have included sensitivity analysis results on the explovation-exploiaatioo tradeoff function for the CelebA and datasets in the following Table T2 The observed trends are consistent with those reported in Table 5 of the main paper. These additional findings further strengthen our hypothesis regarding the role of the exploration-exploiatii tradeoff function.
Table 12: DiffATD's Performance Across Varying with B = 200
Active Discovery of Handwritten Digits
Dataset
0.2
a 1.0
CclebA
0.4193
0.4565
0.4258
MNIST
0.9227
0.9682
0.9459
I Rationale Behind Uniform Measurement Schedule Over the Number of Reverse Diffusion Steps
We adopt a uniform measurement schedule across all denoising steps, and this design choice is deliberate. A non-uniform schedule with fewer measurements at higher noise levels and more frequent measurements lower noise levels might seem intuitive, but is less effective. By the time the noise level is low, the image structure is largely formed, and overly frequent measurements at that
31

---

stage do not provide additional value, as they limit the diffusion model's ability to adapt meaningfully based on the measurements. Instead, uniform schedule ensures that measurements are distributed evenly, giving the diffusion model adequate time to adapt and refine its predictions based on each measurement. This balance ultimately leads to more stable and effective reconstructions across diverse settings. On the other hand, non-uniform schedule higher noise levels and fewer at lower noise levels - can be counterproductive. At higher noise levels, the reconstruction is predominantly governed by random noise, making frequent measurements less informative and potentially wasteful.
with more frequent measurements at
J Performance of DifTATD Under Noisy Observations
We evaluate the robustness of DiffATD in the presence of noisy observations by introducing varying levels noise into the observation space. As shown in Tables 13 and 14 DiffATD consistently maintains strong performance across noise levels across different settings, demonstrating its resilience and reliability under imperfect data conditions. To further understand DiffATD's robustness, we visualize posterior reconstructions of the search space from sparse, partially observable, and noisy inputs (Figure 22). Despite the noise, DiffATD effectively reconstructs clean representation of the underlying space, explaining its consistent performance across varying noise levels in the active target discovery task.
Table 13: DiffATD's Performance with MNIST dataset Under Noisy Observation.
Active Discovery of Handwritten Digits
Noise Level
B = 100
B = 150
B = 200
μ=0 and ø 20
0.7318
0.8420
0,9674
μ=0 and a 30
0.7307
0.8401
0.9641
== 10 and 30
0.7298
0.8393
0.9624
No Noise
0.7324
0,8447
0,9682
Table 14: DiffATD's 's Performance with DOTA dataset Under Noisy Observation.
Active Discovery objects, e.g. plane, truck, etc.
White Noise Level
B 200
B 250
300
μ=0 and 20
0.5410
0.6150
0.7297
== and = 30
0.5139
0.6335
0.7384
p=10 and a 30
0.5292
0.6319
0.7269
No Noise
0.5422
0.6379
0.7309
Movaremen: Spacc
Peeriie DMNTD
Suepled Regiees by ZMEATT
4
4
Figure 22: Visualizations of Reconstructed Search Space from Noisy Observations.
32

---

K Species Distribution Modelling as Active Target Discovery Problem
We constructed our species distribution experiment using observation data of lady beetle species from iNaturalist. Center points randomly sampled within North America (latitude 2 to 55.0%N, longitude 123.1 " to 75.0"W). Around each center, we defined a square region approximately 480 km 480 km in size (roughly 5 degrees in both latitude and longitude). Each retained region was discretized into a 64x64 grid, where the value of each cell represents the number of observed lady beetles. To simulate the querying process, each 2x2 block of grid cells treated query. We evaluated our method on real Coccinella Septempunctata observation data without subsampling, Our goal is to find as many Coccinella Septempunctata possible within region.
L Statistical Significance Results of DifFATD
In order to strengthen our claim on DiffATD's superiority over the baseline methods, we have included the statistical significance results with the DOTA and CelebA datasets, and present the results in Tables [6] These results are based on 5 independent trials and further strengthen our empirical findings, reinforcing the effectiveness of DiffATD across diverse domains.
Table 15: Statistical Significance Results with DOTA Dataset
Active Discovery of Objects like Plane, Truck, etc.
Method
B = 100
B = 150
B = 200
RS
0.1990 0.0046
0.2487 + 0.0032
0.2919 + 0.0036
Max-Ent
0.4625 0.0150
0.5524 + 0.0131
0.6091 + 0.0188
GA
0.4586 0.0167
0.5961
0.0119
0.6550 0.0158
DIJAAD
0.5422 0.0141
0.6379
0.0115
0.7309 0.0107
Table 16: Statistical Significance Results with CelebA Dataset
Active Discovery Different Parts Human Faces.
Method
200
250
B 300
RS
0.1938 0.0017
0.2441
0.0021
0.2953 + 0.0002
Max-Fmi
0.2399
0.0044
0.3510
0.0060
0.4498 +
GA
0.2839
0.0106
0.3516 + 0.0110
0.4294 + 0.0121
DifJATD
0.4565 0.0089
0.5646
0.0086
0.6414
0.0081
M
Comparison With Multi-Armed Bandit Based Method
We compare the performance with MAB-based methods across varying measurement budgets, with results summarized in the Table below 17 18 These analyses are conducted the context of active target discovery the MNIST digits and DOTA overhead images, respectively. These MAB-based methods struggle in the active target discovery setting due to their lack of prior knowledge and structured guidance compared to the Diffusion model, resulting in significantly weaker performance than DifTATD.
Table 17: SR comparison with MNIST Dataset
Active Discovery of Handwritten Digits
Method
= 100
B = 150
B = 200
UCB
0.0026
0.0194
0.0923
e-greedy
0.0151
0.0394
0.0943
DiffATD
0.7324
0.8447
0.9682
33

---

Table 18: SR comparison with DOTA Dataset
Active Discovery of Objects in Overhead Images
Method 200
B 250
B 300
UCB 0.1132
0.2487
0.2146
DifFATD
0.5422
0.6379
0.7309
N Segmentation and Active Target Discovery are Fundamentally Different
Tasks
Segmentation and Active Target Discovery (ATD) serve fundamentally different purposes. Segmen- tation techniques operate under the assumption that the full or partial image already available, focusing labeling observed regions. In contrast, ATD is centered around reasoning about unob- served regions using only sparse, partial observations. This distinction is crucial-when only a few pixels are known, in our setting (An illustrative example of this scenario is shown in Figure 23). segmentation models offer little value, since the primary challenge lies not in interpreting the visible content, but strategically exploring and inferring the hidden parts of the search space to maximize the target object discovery.
Initial Input Image
Input After 1 Query
Input After
Input After
2nd Query
3rd Query
Figure 23: Visualization of Search Space initial Active Target Discovery Phase.
More Details on Computational Cost across Search Space
We have conducted a detailed evaluation of sampling time and computational requirements of DifJATD across various search space sizes. We present the results in I9 Our results show that DiffATD remains efficient even the search space scales, with sampling time per observation ranging from 0.41 to 3.26 seconds, which is well within practical limits for most downstream applications. This further reinforces DiffATD's s scalability and real- aol-world applicability.
Table 19: Details of Computation and Sampling Cost Across Varying Search Space Sizes
Active Discovery of Handwritten Digits
Search Space
Computation Cost
Sampling Time (Seconds)
28 x 28
726.9 MB
0.41
128
1.35 GB
1.48
256 x 256
3.02 GB
3.26
P More Visualizations on DiffATD's Exploration Exploitation strategy at Different Stage
In this section, we provide additional visualizations that illustrate how DifJATD balances exploration and exploitation at various stages of the active discovery process. These visualizations are shown in
figures 24
27 28 In each example, we show the exploration score (exp)score ()), likelihood and the confidence score of the reward model (r&) across measurement space
score like
34

---

at two distinct stages of the active discovery process. The top row represents the initial phase (measurement step 10), while the bottom row corresponds near-fima final stage (measurement step 490). We observe similar trend across all examples, i.e., DifJATD prioritizes the exploration score when selecting measurement locations during the early phase of active discovery. Thus, DiffATD aims to maximize information gain during the initial search stage. As the search approaches its final stages, the rankings of the measurement locations shift to being primarily driven by the exploitation score, defined in Equation 7 As the search progresses, the confidence score of Tá becomes more accurate, making the expl Peore () more reliable. This explains DiffATD's growing reliance on the exploitation DiffATD's s exploration strategy, particularly how it dynamically balances exploration and exploitation. These visualizations also underscore the effectiveness of DiffATD in addressing active target discovery within partially observable environments.
in the later phases of the process. These additional visualizations illustrate
Exploration Scora (e)p)wmn)) Skin
Likelihood Scom (lial))-n)) Acroes Meaaanment
Confidence Scorn of Acrose Messuremnt Spuce
Measurement Location Ranked DiEFATD
Across Measurement Spuce
Initial Measurement @
Truth Exploration (eeplee))) Acroes Messurement Space
Likellhood Score (likelsmm0) Across Measuremen: Space
Confidence Score of Acroes Mewsnnmment Space
Measurement Location Ranked by DifAAT
Final Measurement slep @ 49099
Figure 24: Explanation of DiffATD. Brighter indicates higher value and higher rank.
Exploration Score (expl--rg) Actoss Measurement Space
Likelihood (likel)-m))) Across Measurement Space
Confidence ofr,()
Messumement Ranked by DiIATD
Across Measurensent Space
Plane Turger
Initial Meusurement step t= 10
Ground Truth Mask
Explorstio (espi)sng)
Likellhood (likels-*))
Confidence
Acros Mussurement Space
Across Measurement Space
Measurement Space
by
step tx 490
Figure 25; Explanation of DiffATD. Brighter indicates higher value and higher rank.
35

---

Exploration Scom (exph-mn)) Acress Measuremnnt Space
Likelihood Score (likeljene() Across Measurement Space
Confidence Score ry Across Measurement Space
Measureennt Location Ranked by DifATD
Hair, Eyes, Nose, and Lips as Target
Initial Measurement stop
Ground Truth Mark
Exploration Scone (rxp)enn)) Across Measurement Space
Likellhood Score (lkellsm))) Acrass Mearurement Space
Confidence 1 Across Measurement Space
Mrasurement Ranked by DifATT
Final Measurement step t- 490
Figure 26: Explanation of DiffATD. Brighter indicates a higher value, and higher rank.
Exploration Score (mxp!-**) Across Measurement Space
Libelihood Score (like))-))) Across Measurement Space
Confidence Score ty
Measurement Location Ranked by DifIATD
Across Messurement Space
Plane Bargei
Initial Measurement step t= to
Ground Truth Mask
Exploration (explren))
Score (likelswon))
Confidence (0)
Across Measurement Space
Acrosa Messurement Squoe
Across Measurement Space
Banked by DifEATD
Measurement step t= 490
Figure 27: Explanation of DifJATD. Brighter indicates higher value, and higher rank.
36

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Fisploraion Scor (rxphhnng) Acroes Measurement Space
Tikelihond Score (liel))me)) Across Messurement Space
Confidence Seor of 1 Acroes Measuremen Space
Messurement Location Ranked by DifFATD
Truck Target
Initial Measurement
Exploration Scone (mxp)em))) Across Measuueeeet Space
Likelihood Score (lkee))omg) Across Meosurement Space
Confidence Stone of f, Auruss Measurement Space
Meavurmment Loration Ranked by DifFATD
Final Measurement step t- 490
Figure 28: Explanation of DiffATD. Brighter indicates a higher value, and higher rank.
Importance of Utilizing a Strong Prior in Tackling Active Target Discovery
The purpose the prior belief model (e.g., a pretrained Diffusion model) in DiffATD construct dynamically updated, uncertainty-ave aware belief distribution over unobserved regions-critical critical for guiding the exploration-exploiiaae belief model that is capable of understanding the hidden structure of the underlying search space. In order validate this, we conduct an experiment with different choice of the prior belief model that is trained on a different domain (i.e., ImageNet), and compare its performance with DifFATD where the prior belief model is trained on the same domain (i.e., DOTA). J. We present the result in the following Table 20) Our empirical observation further reinforces the fact that leveraging strong prior belief model crucial for efficiently tackling active target discovery.
tradeoff in target discovery. Thus, important utilize
Table 20: SR comparison with DOTA Dataset
Active Discovery of Objects from Overhead Imagery
Method
B 250
B 300
DifFATD with weak prior Model DifFATD
0.5143
0.6391
0.6379
0.7309
R
Notation Table
To prevent ambiguity, we include below a compact notation table summarizing all symbols and variables used in describing the DiffATD methodology.
Table 21: Notation summary for the DiffATD framework.
Notation
Description
Predicted or estimated search space at the I-th observation step. Set of previously observed partial glimpses of the search space up to step
Zx
a(()
i-th element in the batch of particles (superscript (i) denotes particle index). Measurement location the t-th time step.
q1
Q
Set of measurement locations to time step L.
T
Time step index the reverse diffusion process.
37

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S Limitations and Future Work
While DiffATD demonstrates strong efficiency addressing active target discovery tasks across diverse settings, it currently depends on the availability of robust domain-specift prior model to perform effectively. This requirement can be restrictive in real-world applications such rare species identification or rare disease discovery, where data scarcity makes it difficult to establish a reliable prior. Consequently, the method's success is inherently linked to the quality and expressiveness of the prior model. In future work, we aim to extend DifFATD toward settings with weak or no prior knowledge, enabling active target discovery under an uninformative prior.
38


Reviews:
[{"review_id": "r9VIB6Cxlm", "reviewer": "Reviewer_K1iz", "summary": "To address the challenge of identifying targets of interest in partially observable environments while minimizing costly ground-truth feedback, this paper introduces Diffusion-guided Active Target Discovery (DiffATD). The approach leverages Tweedie’s formula to construct a belief distribution over unobserved regions. Using this distribution, the method employs an exploration-exploitation strategy: exploration is guided toward regions with high entropy, while exploitation targets regions with low entropy. Experiments are conducted to demonstrate the effectiveness of the proposed approach.", "questions": "Please refer to Strengths and Weaknesses Section", "limitations": "The authors does not seem to include the Broader impacts and Limitations of their work. Some of the impacts of this work could be in domains like medical imaging, ecological species discovery, and remote sensing. In terms of the limitations, the proposed approach  may have higher computational cost which should be discussed in this paper.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "*Strengths:* \n\n* The authors effectively articulate the motivation of their approach in the introduction section, particularly in comparison to standard reinforcement learning methods, emphasizing its advantage in reducing labeling costs.\n* Figure 1 clearly illustrates the role of the exploration-exploitation strategy in efficiently identifying the target of interest.\n* The proposed methodology is grounded in  theoretical foundations and appears to offer a novel contribution.\n* The approach may offer  impact in domains such as medical imaging, species discovery, and remote sensing, where labeling is costly and limited.\n* An ablation study is conducted to demonstrate the contribution of individual components—specifically, exploration and exploitation—to the overall performance.\n\n\n*Weaknesses:* \n* The baseline comparisons are limited. Aside from random search and internal ablations (exploration-only and exploitation-only), no competitive baselines are included. The authors should compare against stronger alternatives where applicable [1–3]. If not applicable, authors need to provide the reason for that. \n* The results for the fully supervised approach such as FullSEG should be included as part of the all 3 datasets (Overhead Imagery, Species, Skin Disease).\n* Multi-armed bandit methods like Upper Confidence Bound (UCB) are not considered as baselines. Given their relevance, the authors should include such methods across all datasets to provide a more comprehensive comparison.\n* Some notations are unnecessarily long and could benefit from simplification for readability. For instance, symbols like e.g., $exploit^{score} (q_t)$, $likeli^{score}(q_t)$  in Equation 7 may be renamed for clarity.\n* Certain references appear to be missing. For example, the refer to the  proof aboveTheorem 3 is marked with “??”. \n* Figure captions lack sufficient detail. Specifically, Figure 2 would benefit from a more comprehensive explanation of the DiffATD framework, rather than the generic caption “An Overview of DiffATD.”\n* The function of the parameter $\\kappa (\\mathcal{B})$  in Equation 9, which balances exploration and exploitation, is not visualized. Including a plot or illustration of this function would improve interpretability.", "was_revised": true, "final_justification": "The authors have addressed some of my concerns. While I acknowledge the paper presents some novel contributions, it still lacks in terms of the comprehensive evaluation considering all relevant baselines. Taking this into account, I am updating my score to a Borderline accept.", "rebuttal": "Thank you for your valuable feedback. We've addressed all your comments and concerns.\n\n\n> Q1: The authors should compare against stronger alternatives where applicable [1–3]. If not applicable, authors need to provide the reason for that.\n\n**A1:** Thank you for your question. However, methods [1-3] are not applicable for the following two key reasons (We refer to our discussion on Lines 79-84):\n* **(1)** All these prior methods typically focus solely on optimizing for reconstruction, while our ultimate goal is identifying target-rich regions within a pre-specified budget. Success for our task hinges on balancing exploration (obtaining useful information about the scene) and exploitation (uncovering targets).\n* **(2)** In ATD problem setting, targets are not pre-defined, meaning there is no ground-truth labeling or even a pre-specified definition of the reward signal before discovery during inference, whereas RL-based methods [1-3] rely on extensively pre-defined rewards and supervised training, making them not applicable for ATD.\n\n> Q2: The results for the fully supervised approach such as FullSEG should be included as part of the all 3 datasets (Overhead Imagery, Species, Skin Disease).\n\n**A2:**  It is a nice observation. In Table 5, we have included results with fully supervised approaches such as FullSEG for both the overhead imagery (DOTA) and skin disease datasets, as these tasks are derived from computer vision and support traditional segmentation-based evaluation. To further assess the generalizability of our method beyond vision-based domains, we also evaluated it on the species discovery task. This task is fundamentally different—it is formulated as active discovery over an unobserved spatial distribution and does not lend itself to segmentation-based approaches. As a result, fully supervised methods like FullSEG are not applicable in the species discovery setting. We appreciate your feedback and hope this clarifies our evaluation approach. \n\n> Q3: MAB methods like Upper Confidence Bound (UCB) are not considered as baselines. Given their relevance, the authors should include such methods across all datasets to provide a more comprehensive comparison.\n\n**A3:** We appreciate the suggestion. Multi-armed bandit methods such as UCB are fundamentally incompatible with the ATD setting. ATD operates under a partially observable environment, its objective is to strategically cover a large, structured environment where observations are strongly correlated, under a strict budget. In contrast, MAB assumes independent arms with stationary reward distributions and focuses on maximizing cumulative reward, assumptions that do not hold in ATD.\n\nNevertheless, we included experiments with MAB-based baselines in our study by implementing both UCB and $\\epsilon$-greedy strategies. Their performance under the ATD setting is reported in **Appendix T, Table 17**. Furthermore, we conduct several additional experiments on DOTA dataset, results are shown in the table below. As shown in both of the tables, MAB methods such as UCB perform poorly in the ATD setting, confirming their incompatibility with this problem. \n\n**Comparison with UCB on DOTA**\n\n|     Method      | $\\mathcal{B}=200$ | $\\mathcal{B}=250$ | $\\mathcal{B}=300$ |\n|----------------------------|------------------|-----------------|--------|\n| UCB (Bandits) |  0.1132 |  0.2146 |  0.2487   | \n| DiffATD |  0.5422  |    0.6379   | 0.7309 |\n\n\n> Q4: Some notations are unnecessarily long and could benefit from simplification for readability. For instance, symbols like e.g., , in Equation 7 may be renamed for clarity.\n\n**A4:** We appreciate your feedback. We will simplify these notations to help readers follow the content more easily.\n\n> Q5: Certain references appear to be missing. For example, the refer to the proof aboveTheorem 3 is marked with “??”.\n\n**A5:** Thank your for the observation, we will correct this typo.\n\n> Q6: Figure captions lack sufficient detail. Specifically, Figure 2 would benefit from a more comprehensive explanation of the DiffATD framework, rather than the generic caption “An Overview of DiffATD.”\n\n**A6:** Thank you for the suggestion!  We will certainly add more details in the caption.\n\n\n> Q7: The function of the parameter in Equation 9, which balances exploration and exploitation, is not visualized. Including a plot or illustration of this function would improve interpretability.\n\n**A7:** Thank you for highlighting this valuable point. The parameter $\\kappa(\\beta)$ serves as a scheduling function to balance exploration and exploitation, as described in lines 200–204. We also analyze its sensitivity in **lines 271–280 and in Table 4**. We fully agree that visualizing the behavior of $\\kappa(\\beta)$ would greatly enhance interpretability. In response to your suggestion, we will include a dedicated figure in the revised manuscript to clearly illustrate the schedule function and help readers better understand its practical influence on the method’s performance.\n \n> Q8: The authors does not seem to include the Broader impacts and Limitations of their work. Some of the impacts of this work could be in domains like medical imaging, ecological species discovery, and remote sensing. In terms of the limitations, the proposed approach may have higher computational cost which should be discussed in this paper.\n\n**A8:**  Thank you for your suggestion. We recognize the importance of discussing both the broader societal impacts and the limitations of our work. In terms of broader impacts, We agree that DiffATD has broader implications beyond medical imaging, remote sensing and species discovery, such as drug discovery and hazardous industrial pollution monitoring. We will include a dedicated section in the revised manuscript to articulate these broader implications more clearly. With regard to limitations, we fully agree that computational cost is an important consideration. To address this, we have measured the computational cost-both inference time and memory cost-across different scales of the search space and provided a detailed analysis in **Appendix V, Table 18**."}, {"review_id": "aN5hUdf1Xw", "reviewer": "Reviewer_uQyE", "summary": "The paper studies active target discovery where items have to be found across a domain. The paper proposes DiffATD, which maintains a belief distribution over unobserved states. DiffATD then selects new observations by carefully balancing exploration and exploitation. The paper evaluates DiffATD across of item \"discovery\" examples with images. Across those examples, DiffATD outperforms uniform pixel-selection and variants based around pure exploration or pure exploitation.", "questions": "* The paper does not ablate the choice of belief model experimentally. Is the choice of single-step diffusion important?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n* The idea of balancing exploration and exploitation for active target discovery appears novel and interesting.\n* The proposed method significantly outperforms baselines across all experiments. The experimental methodology appears solid, although experiments are small-scale, and are not comparing to many baselines. I am not familiar enough with the subfield to say conclusively whether any particular baselines are missing.\n\nWeaknesses:\n* The key weakness in my eyes is the omission of a comparison to methods from bandits / Bayesian optimization. It seems to me that the problem could be modeled as a noise-free bandit problem. If modeled as a bandit problem, one could build upon a wide range of prior literature that studies how to effectively balance exploration and exploitation. There are a plethora of methods, for example, also some information-based methods such as \"information-directed sampling\" [1] which seems related to the proposed method.\n* The paper is not including any theoretical guarantees for the sampling scheme, as opposed to prior results from bandits / BayesOpt.\n* The term $\\kappa(B)$ from the sampling objective depends on the remaining budget $B$. This seems undesirable to me, as often a budget is not clearly defined (e.g., search and rescue from the motivation). Often, we simply want to identify the target \"as quickly as possible\". Many bandit algorithms do not require specification of a budget upfront, yet still provide anytime optimality guarantees.\n\nTypos:\n* lines 190: \"??\"\n\n[1]: Russo & Van Roy. Learning to Optimize via Information-Directed Sampling.", "was_revised": true, "final_justification": "The authors adequately clarified some of my main concerns during the rebuttal, and I therefore increase my score to 4. Nevertheless, I agree with the other reviewers that the submission lacks some clarity and that results are quite scattered (especially in the appendix).\n\nAlso, the authors did not address my concern about a lack of a theoretical analysis of the proposed method (in simpler settings), which could significantly strengthen the paper in my view.", "rebuttal": "Thank you for your valuable feedback. We've addressed all your comments and concerns below.\n\n> **Q1:** The key weakness in my eyes is the omission of a comparison to methods from bandits / Bayesian optimization. It seems to me that the problem could be modeled as a noise-free bandit problem. \n\n**A1:** Thank you for raising this important point. While, at first glance, active target discovery (ATD) and (noise-free) bandit problems seem related—both balancing exploration and exploitation—there are deep, structural differences that make direct application of classic bandit based methods fundamentally inadequate for ATD. **The fundamental bottleneck is that the action space in MAB cannot capture the structural semantics of the environment, which themselves define the targets**. Below, we clarify these differences with concrete arguments and supporting experimental results.\n\n1.**Modeling Paradigm: Environment-Structure-Centric vs. Action-Centric**\n\n\nIn the domains targeted by ATD, such as medical imaging and species discovery, the environment embodies a complex, domain-specific structure that is challenging to accurately represent solely through action correlations—whether during the initial modeling of the MAB problem or throughout the online learning process. **Such structural semantics fundamentally dictates whether a given query corresponds to a target, making such semantics indispensable for accurate discovery. Consequently, these problems inherently require environment-centric modeling,** underscoring the need for a generative model capable of explicitly representing such structured priors. Furthermore, ATD operates in a partially observable environment, where observation correlations stem from the inherent structure of the environment rather than from the actions themselves. In contrast, MAB problem modeling, even when incorporating correlations among actions, fails to capture these environment-driven dependencies.\n\n* Active Target Discovery: **Each sampling action potentially informs about its neighbors and influence the estimation of the global environment structure; spatial or semantic correlations are intrinsic.** Feedback from one region impacts the belief about other unobserved regions, and efficient strategies build a coherent model of global structure.\n\n\n2.**Objective: Novelty in Discovery vs. Cumulative Reward**\nThe modeling objective of ATD also fundamentally differs from that of bandit formulations.  \n* Active Target Discovery: The sole aim is to **strategically discover as many new targets as possible within a fixed sampling budget**. Unlike Bandit, in ATD, Sampling the same location twice yields no additional value; **novelty and strategic search space coverage are critical.** For example:  In ATD (e.g., searching for rare tumors in an MRI), revisiting the same region after a tumor has been found offers no new benefit.\n\nNevertheless, despite the different objectives, one can still frame the ATD problem as an MAB formulation without repeated queries (e.g., as a noise-free MAB). We conducted several experiments by modeling the ATD problem as a multi-armed bandit formulation on the simplest MNIST-based scenario in **Appendix T, Table 17**, which demonstrate that under the ATD objective, the absence of explicit modeling of the environment’s structural semantics leads to failure in correctly discovering novel targets. We also compare the performance of UCB and DiffATD using the DOTA dataset (Please see the table below). These additional results further reinforces the incapability of standard bandit based approach in ATD setting.\n\n**Comparison with Multi-Armed Bandit (UCB) on DOTA**\n\n|     Method      | $\\mathcal{B}=200$ | $\\mathcal{B}=250$ | $\\mathcal{B}=300$ |\n|----------------------------|------------------|-----------------|--------|\n| UCB |  0.1132 |    0.2146   | 0.2487 |\n| DiffATD |  0.5422  |    0.6379   | 0.7309 |\n\nNevertheless, it could be an interesting direction for future work to investigate how to explicitly incorporate environmental structural semantics and discover new targets into the MAB framework.\n\n> **Q2:** The term $\\kappa(\\beta)$ from the sampling objective depends on the remaining budget. This seems undesirable to me, as often a budget is not clearly defined (e.g., search and rescue from the motivation). Often, we simply want to identify the target \"as quickly as possible\".\n\n**A2:** **$\\kappa(\\beta)$ Does Not Preclude Anytime Use: The mechanism involving $\\kappa(\\beta)$ can be generalized or made anytime by considering it as a monotonically decreasing function of elapsed time or queries made, rather than as a function of a strictly known budget.** One can, for instance, design $\\kappa(.)$ to smoothly balance exploration/exploitation based on the number of queries so far, regardless of an explicit stopping point. Moreover, our framework can flexibly accommodate fixed-budget, rolling-budget, or open-ended (anytime) objectives by appropriately designing or learning $\\kappa$(·). In our experiments, we use a simple function for simplicity and clarity in the discussion and domain alignment, but the scheme does not assume strict foreknowledge of a terminal budget. If, for example, the “budget” is unbounded but we wish to “find the target as fast as possible”, $\\kappa$(·) can be defined to sustain exploration longer, or adaptively decay based on observed rates of discovery. To conclude, $\\kappa(.)$ is a design choice and depends on the specific requirements of the problem at hand. \n\n\n> **Q3:** Typos in line 190\n\n**A3:** We apologize for the typo. We will fix the typos in the final version of the paper.\n\n> **Q4:** The paper does not ablate the choice of belief model experimentally. Is the choice of single-step diffusion important?\n\n**A4:** Thank you for the question. \n* The purpose of the belief model (e.g. Diffusion model) in DiffATD is to construct a dynamically updated, uncertainty-aware belief distribution over unobserved regions—critical for guiding the exploration-exploitation tradeoff in target discovery. **Thus, it is important to utilize a belief model that is capable of understanding the hidden structure of the underlying search space.**\n* In order to validate this, following your feedback, we conduct an experiment with a different choice of the belief model that is trained on a different domain, and compare its performance with DiffATD where the prior belief model is trained on the same domain. We present the result in the following table. \n\n**Effect of Prior Belief Model on Performance ( On DOTA)**\n\n|     Method     | $\\mathcal{B}=250$ | $\\mathcal{B}=300$ |\n|----------------------------|-----------------|--------|\n| DiffATD with a weak prior model |    0.5143   | 0.6391 |\n| **DiffATD** |    **0.6379**   | **0.7309** |\n\n\nOur experimental outcomes indicate that the search performance drops significantly when prior belief model is not capable of capturing the hidden structure of the underlying search space, highlighting the importance of a strong belief model (i.e. a pretrained diffusion model) in tackling Active target discovery. \n\nWe would also like to highlight that we utilize Tweedie's formula to reconstruct the search space from a noisy image in a single-step, making the inference process significantly faster and saves significant computation time."}, {"review_id": "7cHA0or3Rt", "reviewer": "Reviewer_QyUe", "summary": "This paper investigates the target discovery problem with a limited computational budget.\nSpecifically, leveraging the generative capacity of diffusion models, this paper introduces DiffATD, which utilizes diffusion dynamics for efficiently active target discovery with a limited sampling budget and better interpretability.\nExperimental results show that DiffATD outperforms baselines in various benchmarks.", "questions": "### Questions\n1. Could the authors provide a comparison with the other existing search algorithms?\n2. Could the authors provide a comparison with the other existing objective detection methods?\n3. Could the authors explain the relationship between the proposed method and information bottleneck?", "limitations": "No. Comparison with existing search algorithms (e.g., MCTS) and objective detection methods.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths\n1. Interesting problem settings and well-defined problem formulation from the perspective of entropy and mutual information.\n\n### Weakness\n1. Comparison with other search algorithms (e.g., MCTS and UCB).\n2. Comparison with other objective detection algorithms.\n3. Could the authors explain the relationship between the proposed method and information bottleneck?\n\n### Typos\n1. Lines 190: proof in ??\\\n2. Lines 234: Active Discovery of Species.\n3. Lines 244: Active Discovery of Skin Disease.\n4. Lines 271 and 293: Same issues", "was_revised": true, "final_justification": "I have read the response and other reviews. My concerns have been addressed properly, thus I tend to raise my score to borderline accept.", "rebuttal": "Thank you for your nice questions and feedback. We have addressed all your comments and concerns below.\n\n> Q1: Could the authors provide a comparison with the other existing search algorithms (e.g., MCTS and UCB)\n\n**A1:** Thank you for your valuable feedback. To compare with other search methods, we included experiments with multi-armed bandit baselines by implementing **both UCB and $\\epsilon$-greedy strategies**. Their performance under the ATD setting is reported in **Appendix T, Table 17**. We have also provided additional comparative results with UCB using DOTA dataset (See the table below). These results indicates that incapability of UCB based approaches in tackling ATD task. Next, we illustrate why MCTS, UCB based approaches are not applicable in active target discovery setting.\n\n* ATD operates under a partially observable environment where the objective is to **strategically cover a large, structured space** under a strict budget, and **observations' semantics are highly correlated**. In contrast, MAB assumes independent arms with stationary reward distributions and focuses on maximizing cumulative reward---assumptions that do not hold for ATD.\n*  MCTS, on the other hand, relies on repeated rollouts in a known or simulatable environment to estimate long-term rewards. However, in ATD problem, observations **can only be obtained through costly real queries, and rewards are defined online rather than pre-specified**. These characteristics make MCTS fundamentally inapplicable to ATD.\n\n**Comparison with UCB on DOTA**\n\n|     Method      | $\\mathcal{B}=200$ | $\\mathcal{B}=250$ | $\\mathcal{B}=300$ |\n|----------------------------|------------------|-----------------|--------|\n| UCB (Bandits) |  0.1132 |  0.2146 |  0.2487   | \n| DiffATD |  0.5422  |    0.6379   | 0.7309 |\n\n> Q2: Could the authors provide a comparison with the other existing objective detection methods\n\n**A2:** Thank you for this question. We would like to clarify why traditional object detection methods are not directly comparable or applicable to the Active Target Discovery (ATD) problem due to fundamental differences:\n\n* **Limited and Incremental Observability:**\n**In ATD, the agent only has access to sparse, sequential observations from a large, partially observed environment (See Figure 1)**. The goal is to strategically explore and identify target-rich areas without ever fully observing the entire space. In contrast, **object detection methods operate on fully observed images where all visual information is available upfront**. This key difference means object detectors are not designed to handle the sequential, budget-constrained querying and discovery aspects central to ATD.\n\n* **Lack of Predefined Targets and Labels:**\nObject detection relies heavily on supervised learning with extensive labeled datasets where object classes and bounding boxes are known beforehand. Conversely, ATD assumes no prior knowledge or labeled data about the targets. Target properties unfold dynamically as queries are made, requiring an adaptive, online learning approach. Our DiffATD framework is specifically designed to learn from this limited, sequential feedback without requiring any labeled training data, unlike standard object detection pipelines.\n\nFor these reasons, while object detection methods excel in fully supervised, fully observed settings, they are not suitable baselines for the ATD problem. We hope this clarifies the fundamental distinctions and justifies our methodological choices.\n\n\n> Q3: Could the authors explain the relationship between the proposed method and information bottleneck?\n\n**A3:** Thank you for the question. Our method does not apply the Information Bottleneck principle. Although both approaches share information-theoretic notions such as entropy, our work focuses on designing an active querying strategy to discover more targets in a partially observable environment under strict budget constraints, while Information Bottleneck aims to learn compressed representations that retain task-relevant information. Our formulation does not optimize an Information Bottleneck objective and differs fundamentally in its goal and application.\n\n> Q4: Typos in Lines 190, 234, 244, 271 and 293\n\n**A4:** Thank you for the observations, we will correct the citation typo."}, {"review_id": "dQbLLnYp8Z", "reviewer": "Reviewer_GeQD", "summary": "The paper proposes a novel method, DiffATD, to guide diffusion models in task discovery. To this end, following existing ideas from experimental design, DiffATD trades off between exploration of novel areas in the search space, measured by (an approximation of) the model's entropy, to exploitation of a reward that is learned during the learning process.", "questions": "* Where do you get the rewards from in your experiments? You motivate DiffATD with problems in which labeled data (for supervised learning) is expensive; however, in your experiments it seems like the reward is given by some ground-truth data that was collected offline. Can you please clarify that?", "limitations": "The authors did not mention any limitation of their method DiffATD, answering in the submission guideline:\n> Does the paper discuss the limitations of the work performed by the authors? We design a novel algorithm for a new task.\n\nI believe some more comprehensive discussion on how one can improve DiffATD and what were the challenges in making it work would improve the paper.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n* The problem is important; DiffATD might be useful in more complex domains (such as robotics) for task discovery.\n* The experiments are very comprehensive, showing solid results across several independent tasks.\n* I am not an expert in this field, but the proposed method seems novel.\n\n## Weaknesses\n* Experiments that demonstrate task discovery beyond vision-related tasks (e.g. drug discovery or robotics) would significantly strengthen the paper.\n* The main empirical results of the paper essentially only ablate DiffATD's exploration and exploitation components, comparing against max-entropy, greedy and uniform sampling. The paper only compares DiffATD with multi-armed bandits techniques (UCB and $\\epsilon$-greedy) on MNIST in the appendix. Additional experiments showing demonstrating DiffATD's superiority compared to more competitive methods will improve the paper. For instance, comparing with a baseline that relies on supervised learning (as mentioned in the related works), and showing that DiffATD is much more sample efficient would strengthen the paper.\n* My understanding is that most experiments were carried out only on one seed, with the exception of the experiment in appendix S, which studies only two datasets and lacks comparison against other existing baselines in the literature.", "was_revised": true, "final_justification": "The authors have clarified most of the initial concerns I had about their paper.", "rebuttal": "Thank you for your insightful feedback. We are excited that you found our problem is important, the experiments are comprehensive and the method is novel. We have addressed all your comments and concerns below.\n\n> **Q1:** Experiments that demonstrate task discovery beyond vision-related tasks (e.g. drug discovery or robotics) would significantly strengthen the paper.\n\n**A1:** Thank you very much for this valuable suggestion. We would like to highlight that we have already demonstrated the effectiveness of DiffATD beyond vision-related tasks through **our experiments on species discovery, as shown in Table 2 and Figure 4**. This setting involves non-visual, spatial data and confirms the broad applicability of our approach. We also wholeheartedly agree that extending DiffATD to impactful domains such as drug discovery or robotics is a promising and exciting direction. We look forward to exploring these important areas in our future work and believe DiffATD could offer significant benefits there as well. \n\n> **Q2:** Additional experiments showing demonstrating DiffATD's superiority compared to more competitive methods will improve the paper. For instance, comparing with a baseline that relies on supervised learning (as mentioned in the related works), and showing that DiffATD is much more sample efficient would strengthen the paper.\n\n**A2:**  Thank you for this question. We would like to emphasize that our active target discovery (ATD) problem setting fundamentally assumes the absence of any supervised data prior to deployment, making supervised learning approaches inherently inapplicable. This reflects realistic constraints in many real-world domains—such as medical imaging or species discovery—where obtaining labeled ground-truth data is costly, time-consuming, or simply infeasible. Importantly, even when we hypothetically apply a supervised learning approach by assuming access to ground-truth annotations in our ATD setting, our method, DiffATD, performs comparably—and in several cases even surpasses—the supervised baseline. This is achieved **without requiring any labeled data** (see lines 281–292 and Table 5 in our paper), highlighting the robustness and effectiveness of our approach. This highlights DiffATD’s strong potential to enable effective, interpretable active discovery in practical, data-scarce scenarios.\n\n\n> **Q3:** My understanding is that most experiments were carried out only on one seed, with the exception of the experiment in appendix S, which studies only two datasets and lacks comparison against other existing baselines in the literature.\n\n**A3:** We wish to clarify that all experiments reported in our paper were conducted over three independent runs with different random seeds, and the mean results are presented. Furthermore, Appendix S (Tables 15 and 16) includes the corresponding standard deviations, which illustrate the stability and consistency of DiffATD across these trials. We hope this clarifies the robustness of our experimental evaluation.  \n\n> **Q4:** Where do you get the rewards from in your experiments? You motivate DiffATD with problems in which labeled data (for supervised learning) is expensive; however, in your experiments it seems like the reward is given by some ground-truth data that was collected offline. Can you please clarify that?\n\n**A4:**  Thank you for raising this important question. In our experiments, the rewards are obtained directly as outcomes from each query or observation made during the active target discovery process. It is important to clarify that, unlike conventional supervised learning, **we do not rely on any pre-collected ground-truth labels or offline datasets**. Instead, our method continuously learns a parametric reward model incrementally, using the data gathered sequentially and exclusively during the online active discovery phase at inference time.  \n\n> **Q5:** The authors did not mention any limitation of their method DiffATD. I believe some more comprehensive discussion on how one can improve DiffATD and what were the challenges in making it work would improve the paper.\n\n**A5:** Thank you for raising this point. We will certainly include a Limitation and Future Work section in the updated draft as you suggested."}, {"review_id": "sKOd0EXPLf", "reviewer": "Reviewer_u9fh", "summary": "In scanning problems such as MRI imaging, the data are locally acquired and one would actively decide the targeted scanning area (it is expensive to have a comprehensive scan). In such problems, it is difficult to train a decision maker to guide the scanning process, because fully scanned data are scarce. To this end, this paper considers the scanning steps as denoising steps in the context of a diffusion model. The authors use the diffusion model to build distribution on predictive space at different area. Then, one may leverage the distribution to guide the information gained by scanning different grids, may the information be exploration or exploitation.\n\n**Contributions:**\n- cast scanning decisions into diffusion dynamics.\n- apply exploitation and exploration heuristics leveraged by the Bayesian experimental design community.", "questions": "**Clarification:**\n- Could you please elaborate how the generative $\\hat{x}_t^{i}$ conditioned on the observations $\\tilde{x}_{t-1}$? Does equation (3) indicate this or from which equation may I see this?\n- In Thm 1, why do you have [ \\hat{x}_t^{i} ]_{q_t} ? I thought $\\hat{x}_t^{i}$ is already the $i$-th grid, but do we use grid $q_t$ to index $\\hat{x}_t^{i}$?\n- In line 159, it seems like the aim here is to avoid computing all possible grids. How is this actually achieved by Thm 1?\n- In Thm 1, how strong is the assumption $\\alpha_i = \\alpha_j$ and is this assumption limiting in practice?\n- Could you elaborate why equation (7) and appendix line 434 are valid? I mean, if both the reward and the negative entropy are non-negative, then the product scales in the same direction of the two factors. But if either of them spans across positive and negative values, then optimizing the product is not the same as optimizing the reward and the negative entropy.\n\n**Minor:**\n- You use $Q_t = q_0, …, q_t$ in the paper. However, $q_0, …, q_{t-1}$ were from the past and are actually fixed while decision $q_t$ is optimized. I would suggest writing $Q_{t-1}, q_t$ instead to be clearer on the distinction.\n- Code: When you attach the code, you may consider removing .git folder. That creates unnecessary tracks and github links (your repo seems anonymous which is fine).\n- Code: you may consider adding versions to requirements.txt, e.g. scipy can sometimes have version issues.", "limitations": "I tend to say one should discuss the computation needed for each query, and maybe discuss the quality of the trained reward function.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The studied problem is important and well-introduced.\n- I find it quite interesting to cast the query steps as diffusion dynamics.\n- The method is evaluated on 3 different test problems. \n\n**Weaknesses:**\n- This paper has a lot of parameters and the notation is very complicated. I personally find section 5 (main method section) quite hard to follow. Perhaps some more description on the intuition would help?\n- If I am not wrong, this method has quite significant online computation for each scanning decision (training reward models, optimizing scores etc). For problems like species discovery, perhaps the online complexity is not a major issue. But for problems like MRI scanning (which is mentioned repeatedly in the paper), online computational time is a limitation, and the authors might really need to discuss this. Online complexity is a very common problem in Bayesian experimental design.\n- It seems to me that there are a lot of hyperparameters and models to be tuned. Like exploration weight, $\\kappa(\\cdot)$, and more. This would make it rather complicated to apply the method. For instance, table 4 shows that the SR drops to 0.8465 with $\\alpha = 0.2$ while in table 3 we see that the baseline GA is 0.8261 (I wonder whether the authors conducted statistical tests over repeated experiments? Or were all experiments only run once?).\n- It seems that the algorithm relies on the reward function to correctly identify the target area, while the reward function is trained as the scanning proceeds. One might need to discuss model misspecification problem (e.g. bad model $\\rightarrow$ bad query, bad query $\\rightarrow$ bad model).\n- In addition, if I am not wrong, the reward function is a black-box function, while in the introduction the authors claim white-box policy, which might be exaggerated.\n\n**Clarification:**\n- Could you elaborate why equation (7) and appendix line 434 are valid? I mean, if both the reward and the negative entropy are non-negative, then the product scales in the same direction of the two factors. But if either of them spans across positive and negative values, then optimizing the product is not the same as optimizing the reward and the negative entropy.", "was_revised": true, "final_justification": "My original review listed issues like: clarity, discussion on complexity etc.\n\nThe rebuttal clarified some terms, and made promise to add some discussion on e.g. online complexity.\n\nOne flaw I notice: the authors put a lot of additional experiments in the appendix, but at the moment it seems to me that information is somewhat scattered. I would say the authors need to provide at least an overview in the supplementary, discussing what is in which appendix section, and how the appendix section strengthen the main paper.\n\nMy original rate was already positive (4). and I feel the same score applies. I think this paper is between 4 and 5, more leaning towards 4 because the overall clarity can still be improved, just in my opinion.", "rebuttal": "Thank you for your insightful feedback. We are glad to find our problem important and our method interesting. We have addressed all your comments and concerns below.\n\n> Q1: More description on the intuition would help?\n\n**A1:**. We acknowledge that Section 5 contains numerous parameters and complex notation, which may pose challenges for readers. To enhance clarity, we will add a detailed notation table in the appendix that clearly defines each symbol and its purpose. \n\n> Q2: For problems like MRI scanning, online computational time is a limitation, and the authors might need to discuss this.\n\n**A2:**  We fully acknowledge that online computational efficiency is critical for practical deployment, especially in time-sensitive applications like MRI scanning. To address this, we have evaluated the online computation time required by DiffATD to select the next sampling location across varying search space sizes, using a standard compute setup. These results, detailed in **Appendix Section V** (“More Details on Computational Cost across Search Space”), show that the sampling time per observation ranges from **0.41 to 3.26 seconds**—well within practical limits for many applications, including MRI. We will further emphasize this discussion in the revised manuscript to provide readers with a clear understanding of DiffATD’s online efficiency. \n\n> Q3: Table 4 shows that the SR drops to 0.8465 with $\\alpha=0.2$ while in Table 3 the baseline GA is 0.8261. Whether the authors conducted satistical tests over repeated experiments?\n\n**A3:** Firstly, since the parameter $\\alpha$ governs the balance between exploration and exploitation, it is expected that DiffATD’s performance is sensitive to its choice. Your observation that the Success Rate (SR) decreases to 0.8465 when $\\alpha$—close to the baseline GA’s SR of 0.8261 reported in Table 3—is particularly insightful and aligns well with our intuition. As $\\alpha$ progressively decreases, the model emphasizes exploitation more heavily, leading to a decline in performance. This trend underscores the critical role of exploration during the early stages of the discovery process. Notably, when $\\alpha=0$, the approach effectively reduces to GA, relying solely on exploitation. These results collectively emphasize that a purely exploitation-driven strategy is insufficient for active target discovery, and that maintaining an effective balance between exploration and exploitation is essential for success. \n\nSecondly, we would like to clarify that all results presented in the paper are averaged over three independent trials, with the mean values reported. Additionally, the standard deviations across these trials are provided in **Section S of the Appendix**. These results not only demonstrate the effectiveness of DiffATD but also underscore its stability and consistency across multiple runs.\n\n\n> Q4:  One might need to discuss reward model misspecification problem.\n\n**A4:** We agree that the reward model—trained incrementally as the active discovery process unfolds—plays a pivotal role in guiding exploration and exploitation. We recognize that model misspecification, particularly in the early stages when training data is limited, can lead to suboptimal queries and potentially bias the search process. To address this, DiffATD is designed with a **frontloaded exploration** strategy grounded in the maximum entropy principle. By deliberately selecting the most diverse and uncertain observations early on, we ensure that the reward model is trained on a broad and informative dataset from the outset, thereby reducing the risk of bias and helping correct initial inaccuracies.\n\nAs additional data is acquired with each query, the reward model improves its predictive accuracy, resulting in more reliable guidance for subsequent exploitation-focused queries. This adaptive cycle—where exploration seeds robust model learning, and the refined model in turn enables targeted exploitation—is essential to maintaining both flexibility and effectiveness, even under strict query budgets. To illustrate this, we provide extensive **visualizations (see Figures 7 and 24–28) showing the reward model’s confidence becoming more accurate as the discovery process progresses**, underscoring its critical role in guiding exploitation.\n\n> Q5: The reward function is a black-box function, while the authors claim white-box policy, which might be exaggerated.\n\n**A5:** Thank you for your valuable observation. To clarify, the term “black-box policy” usually refers to policies learned end-to-end via opaque models without explicit interpretability. In contrast, our policy is explicitly designed based on transparent, principled concepts—such as the maximum entropy principle—making it inherently interpretable, which justifies describing it as a “white-box policy.” While the reward model is implemented with a neural network and can be seen as a black-box component, its role is limited to predicting target presence in regions and does not obscure or complicate the policy’s overall interpretability or decision-making logic. We hope this distinction helps clarify our terminology.\n\n> Q6: Are Eqn. 7 and appendix line 434 valid? If both the reward and the negative entropy are non-negative?\n\n**A6:** In our framework, both the reward and the likelihood (which corresponds to the negative entropy) are defined to be non-negative quantities. Specifically, the reward represents the probability that a given region contains the target, so it is naturally bounded between 0 and 1. Meanwhile, the likelihood, as formulated in Theorem 2, involves an exponential function, ensuring it is also always non-negative. Because both factors are non-negative by definition, their product scales consistently with each individual component. Therefore, optimizing the product is equivalent to jointly optimizing both the reward and the negative entropy as intended. We hope this clarifies the validity of Equation (7) and the related expression in the appendix.\n\n> Q7: Discuss computation needed for each query and the quality of the trained reward function.\n\n**A7:**  We have provided a detailed analysis of the computational requirements per query in Appendix Section V, with results summarized in Table 18. Our findings show that DiffATD maintains efficient sampling times—ranging from 0.41 to 3.26 seconds per observation—even as the search space scales, which is suitable for most practical applications. In response to your feedback, we will enhance the manuscript by adding further visualizations, similar to Figures 7 and 24–28, and include a dedicated discussion on the quality and reliability of the trained reward function. \n\n> Q8: In Thm 1, why do you have [$\\hat{x}_t^{(i)}$] $q_t$? Do we use grid $q_t$ to index $\\hat{x}_t^{(i)}$?\n\n**A8:** Here, $(i)$ in the superscript represents $i$'th sample of a batch, and $\\hat{x_t}^{(i)}$ denotes $i$-th sample of the estimated entire search space at the t-th query step (Please see our discussion around Lines 148 -153). Additionally, **yes, we use $[.]_{q_t}$ in the subscript to index $q_t$-th grid/region in the estimated search space $\\hat{x}_t^{(i)}$.** \n\n> Q9: Could you please elaborate how the generative $\\hat{x_t}^{(i)}$ conditioned on the observation $\\tilde{x}_{t-1}$? Does Eqn. (3) indicate this?\n\n**A9:**  Yes, **Eqn. (3) describes how $\\hat{x_t}^{(i)}$ is constructed: it is the denoised estimate of the search space computed via Tweedie’s formula, starting from a noisy latent $x_{\\tau}^{(i)}$.** Crucially, each $x_{\\tau}^{(i)}$ is sampled by executing the reverse diffusion process, which is explicitly conditioned on the set of previously acquired observations { $\\tilde{x}{(t-1)}$ }—this conditioning is reflected in the measurement guidance step of Algorithm 1 (line 6), where the observed values at locations indexed by $Q_{t-1}$ are enforced during the reverse diffusion process. Therefore, the estimated search space $\\hat{x}_t^{(i)}$ integrates all information obtained up to time $t-1$, producing a distribution over possible completions of the unobserved space that is fully consistent with prior measurements. \n\n> Q10: Avoiding computing all possible grids in line 159, how is this achieved by Thm 1?\n\n**A10:** We would like to clarify that our aim is to avoid computing a separate set of $\\hat{x_t}$ for all possible combinations of sampling sequence $Q_t$, not avoiding computation across possible grids $q_t$ at a sampling step $t$. To this end, in Theorem 1, we showed that it is possible to decompose the squared L2 norm inside $\\exp(.)$ term (defined in Eqn. 5) into two parts, one over the indices in $q_t$ (i.e., possible measurement location at time t), and the other over those corresponds to previous observations $Q_{(t-1)}$. We can achieve this by exploiting the structure that the measurement locations $Q_t = Q_{t−1} ∪ q_t$ only differ in the newly selected indices $q_t$. Hence, within the arg max, the elements of each particle $\\hat{x_t}^{(i)}$ remain unchanged across all possible $Q_t$, except at the indices specified by $q_t$. Hence, the term associated with $Q_{t−1}$ becomes a constant in the arg max and can be disregarded. Consequently, the formulation reduces the computing of the squared L2 norms exclusively for the elements corresponding to $q_t$, which can be computed in one shot via a reverse diffusion process because the measurement guidance term in the reverse diffusion process doesn't change as $Q_{(t-1)}$ is fixed.\n\n> Q11: In Thm 1, how strong is the assumption $\\alpha_i = \\alpha_j$?\n\n**A11:** The assumption $\\alpha_i = \\alpha_j$ in Theorem 1 reflects the idea that, when estimating uncertainty over a batch of samples, each sample contributes equally to the computation. In most practical scenarios, especially when there is no prior reason to favor one sample over another within a batch, this is a reasonable and standard assumption, and is common in practical applications."}]

Author rebuttal:

Meta-review: This paper introduces the Active Target Discovery (ATD) problem alongside a solution, DiffATD. It's a creative and well-motivated approach that cleverly uses diffusion models to guide an effective exploration-exploitation search strategy. This work shows promise for applications in fields like medical imaging and remote sensing, and the empirical results convincingly demonstrate its superiority over the tested baselines. The reviewers were ultimately persuaded of the paper's merits, particularly after a thorough and constructive rebuttal from the authors that adeptly clarified the work's contributions. Overall, this is a solid paper.
Decision: Accept (poster)