Active Target Discovery under Uninformative Priors: The Power of Permanent and Transient Memory
Authors: Anindya Sarkar
Binglin Ji
Yevgeniy Vorobeychik
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Model
Active Target Discovery
Primary area: general_machine_learning

Abstract: In many scientific and engineering fields, where acquiring high-quality data is expensive—such as medical imaging, environmental monitoring, and remote sensing—strategic sampling of unobserved regions based on prior observations is crucial for maximizing discovery rates within a constrained budget. The rise of powerful generative models, such as diffusion models, has enabled active target discovery in partially observable environments by leveraging learned priors—probabilistic representations that capture underlying structure from data. With guidance from sequentially gathered task-specific observations, these models can progressively refine exploration and efficiently direct queries toward promising regions. However, in domains where learning a strong prior is infeasible due to extremely limited data or high sampling cost (such as rare species discovery, diagnostics for emerging diseases, etc.), these methods struggle to generalize. To overcome this limitation, we propose a novel approach that enables effective active target discovery even in settings with uninformative priors, ensuring robust exploration and adaptability in complex real-world scenarios. Our framework is theoretically principled and draws inspiration from neuroscience to guide its design. Unlike black-box policies, our approach is inherently interpretable, providing clear insights into decision-making. Furthermore, it guarantees a strong, monotonic improvement in prior estimates with each new observation, leading to increasingly accurate sampling and reinforcing both reliability and adaptability in dynamic settings. Through comprehensive experiments and ablation studies across various domains, including species distribution modeling and remote sensing, we demonstrate that our method substantially outperforms baseline approaches.

Active Target Discovery under Uninformative Prior: The Power of Permanent and Transient Memory
Anindya Sarkar,, Binglin Ji: Yevgeniy Vorobeychik
fanindya, binglin.j. j,, yvorobeychild wwleelttsdleeee Department of Computer Science and Engineering Washington University in St. Louis, USA
Abstract
In many scientific and engineering fields, where acquiring high-quality data is expensive-such as medical imaging, environmental monitoring, and remote sens- ing-strategic sampling of unobserved regions based on prior observations is cru- cial for maximizing discovery rates within a constrained budget. The rise power- ful generative models, such diffusion models, has enabled active target discovery in partially observable environments by leveraging learned priors probabilistic representations that capture underlying structure from data. With guidance from sequentially gathered task-specific observations, these models can progressively refine exploration and efficiently direct queries toward promising regions. However, in domains where learning a strong prior is infeasible due to extremely limited data high sampling cost (such as rare species discovery, diagnostics for emerging diseases, etc.), these methods struggle to generalize. To overcome this limitation, we propose novel approach that enables effective active target discovery even in settings with uninformative priors, ensuring robust exploration and adaptability complex real-world scenarios. Our framework theoretically principled and draws inspiration from neuroscience to guide its design. Unlike black-box policies, our approach inherently interpretable, providing clear insights into decision- making. Furthermore, it guarantees strong, monotonic improvement in prior estimates with each new observation, leading to increasingly accurate sampling and reinforcing both reliability and adaptability in dynamic settings. Through comprehensive experiments and ablation studies across various domains, including species distribution modeling and remote sensing, we demonstrate that our method substantially outperforms baseline approaches.
Introduction
Active Target Discovery (ATD) a fundamental problem in scientific and engineering domains where data acquisition is expensive and environments are only partially observable. Beginning with an unobservable task, the goal is to strategically and sequentially sample glimpses to infer and uncover the underlying target, such as disease regions in medical imaging, pollution hotspots in environmental monitoring, or objects of interest in satellite imagery-all while adhering to strict sampling budget. This task is critical in scenarios like detecting rare tumors in MRT scans, localizing contaminants in remote areas, or identifying missing persons in search-and-reseur missions. In all these cases, the cost of each observation high, and acquiring feedback from the ground- truth reward function often requires expert judgment, specialized equipment, and substantial time. Diffusion-guided Active Target Discovery (DiffATD) M has been recently proposed promising solution the ATD task. It operates by learning strong prior over the search space using samples from the domain of interest.
Equal contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure 1: Interplay of Permanent and Transient Memory to Guide Active Target Discovery.
Specifically, DiffATD [ leverages a diffusion model trained on domain- specific samples to serve as a strong prior, guiding its sampling strategy via learned diffusion dynamics conditioned on the gathered observations to efficiently uncover target regions within constrained sampling budget. This prior-driven approach allows it to balance exploration and exploitation in a principled way, often outperforming baseline methods in well-studied domains. However, the effectiveness of DiffATD II fundamentally hinges on the availability of representative prior samples from the target domain. In many real-world scenarios-sute geographic regions- such samples are either unavailable or prohibitively difficult to obtain. In these cases, the strong prior assumption breaks down, and methods like DiffATD [ struggle to generalize, limiting their applicability in precisely the settings where efficient target discovery is most critical.
emerging diseases, rare environmental hazards, or underexplored
To confront the challenge of ATD without access to prior samples, we draw inspiration from Neuro- science. The real world is inherently dynamic, continually presenting novel and unforeseen situations. Yet, humans navigate such environments seamlessly by drawing on two complementary systems: long-term memory that encodes structured, generalizable knowledge, and a short-term memory that rapidly adapts to immediate context. For instance, when driving in an unfamiliar city, we rely on our understanding of traffic rules (long-term knowledge) while dynamically responding to unexpected road closures or detours (short-term adaptation). Kumaran (2) suggests that this dual mechanism is rooted in the neocortex and hippocampus, that is, the brain leverages a dual memory system encodes structured knowledge
medery-mmdiated comprised of permanent memory- mediated by the neocortex- through slow learning and supports generalization, and transient memory-asssociated with the hip- pocampus-wihn enables rapid acquisition of precise, task-specific information. Inspired by this cognitive mechanism, we argue that emulating such a dual memory structure in artificial agents is essential for solving new tasks in dynamic environments, where both stable generalization and fast adaptability are crucial.
Inspired by this mechanism, we draw on Bayesian inference to tackle ATD in the absence of prior domain data. At the heart of our approach lies an Expectation- Expectation-Maxxmizztionn Maximiaation-sty.eeeeee algorithm that guarantees monotonic improvement of the sampling prior-modeles observations unfold across the environment. This evolving prior actively guides the sampling strategy to maximize discovery under a strict budget. Our prior model architecture reflects mechanisms from the brain's 's dual mull-memory system by pairing a powerful pretrained diffusion model as a long-term or rich, generalizable structure across domains-with lightweight, adaptive module based on Doob's 's h-transform that serves as transient memory, enabling rapid contextual adaptation from new observations. The lightweight Doob's h-transform module is updated after every few observations, allowing it to swiftly adapt to the evolving dynamics of the current task. This synergy enables our system to combine the power of global knowledge with the flexibility of fast local adaptation, allowing for efficient, intelligent exploration in novel and data-scarce environments. Crucially. the integration of a pretrained diffusion model with a lightweight network that implements Doob's 's h-transform enables principled sampling from the posterior distribution conditioned on the accumulated observations. This design ensures that each sampling decision grounded in both prior knowledge and task-specific context, lending theoretical rigor and practical effectiveness to our architecture. Finally, our sampling strategy ranks unobserved points by balancing ex exploration and exploitation scores, driven by an updated prior and an online-trained reward model that learns the target's 's characteristics from gathered observations. As more observations are revealed, the prior progressively improves, leading to more accurate rankings that fuel a highly informed active discovery
diffusion process-av as new
permanent ceemory-capturii

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process, reinforced by theoretical guarantees and compelling empirical evidence. Figure iillstrates the core motivation behind our approach. We summarize our contributions follows:
We introduce a novel and principled framework, Expectation Maximized Permanent Tempo- rary Diffusion Memory (EM-PTDM), designed to uncover targets of interest within a strict sampling budget in partially observable environments. Unlike prior methods, EM-PTDM operates without relying on task-specific prior domain data, significantly broadening its applicabillity. Furthermore, it integrates white-box. box, interpretable sampling policy grounded in Bayesian experiment design, enabling transparent and strategically guided exploration.
EM-PTDM framework is backed by rigorous empirical evidence and ensures monotonic refinement of the prior as new observations are gathered. This continual refinement directly enhances the accuracy of the scoring mechanism used for sampling, resulting more precise and efficient active target discovery over time.
We demonstrate the significance of each component in our proposed EM-PTDM method through extensive quantitative and qualitative ablation studies across range of datasets, including species distribution modeling and remote sensing.
2 Problem Formulation
In this section, we present the details of proposed Active Target Discovery (ATI) task setup. ATD involves actively uncovering one or more targets within a search area, represented as an (initially unobserved) region z divided into N grid cells, such that æ = (xx(1), 2,(2) ...,, x 2. ATD operates under a query budget B, representing the maximum number of measurements allowed. Each grid cell represents a sub-region and serves as a potential measurement location. A measurement of location i provides feedbuck, revealing both the content of a specific sub-region (x(+ for the i-th grid cell, as well as yielding an outcome y( E [0, 1]. where (y()) is the fraction of pixels in the grid cell 20(1) that belong to the target of interest. In each task configuration, the target'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 step as gt, the overall task optimization objective is:
U (x)(()))); {ge} = max Σ y subject to L < B
(4:)
With objective T in focus, we aim develop search policy that efficiently explores the search area (Irest ~ Xieu) to identify as many target regions as possible within a measurement budget B- all without requiring access to any prior samples from the domain of interest.
3 Methodology
A central challenge in ATD under an initially uninformative prior lies in achieving three distinet goals: (1) progressively improving the prior as sequential observations accumulate sinnce the prior fundamentally shapes the ATD process; (2) designing the prior to be swiftly adaptable, capable of rapidly incorporating knowledge from limited observations, as demanded by the task's high data-efficiency requirements, and (3) utilizing the sequentially improved prior model to strategically sample unobserved regions to maximize target discovery within limited sampling budget.
Progressively Improving the Prior model We begin by addressing the crucial challenge of enabling the prior to evolve progressively-enat ensuring that each newly acquired observation from the search space contributes meaningfully to refining the model's understanding and guiding sampling more effectively. To this end, we formulate our approach within the principled structure of the DnnectaaiionMaxiizzaae
(EM) framework, utilizing its iterative inference and optimization steps to systematically refine the prior with each new observation. Specifically, our goal is to learn the parameters of a prior model (e.g., a DDPM), denoted as (3( y), by maximizing the log- evidence log (y) for given observation y. Considering a distribution over observations p(y), this corresponds to maximizing the expected log-evidence, which is equivalent to minimizing the KL divergence between the true distribution p(y) and (z):
6² arg max o
Ep(s)) [log go (v)) = arg min (T.((w)))aa())).
(2)
Next, we derive an iterative optimization procedure for & that ensures monotonic improvement of expected log-evidence Ep(w) [log (2)). We present the result in the following Proposition.
3

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Let dos denote the parameters of the current prior model, then improving this prior by maximizing the expected log-evidence Eyyig) Dog qou [v)] with respect to @n equivalent to maximizing the following surrogate maximization:
Proposition 1.
Φk+1 arg max Ep(s) 40k (alg)
IE
[lgg [x()))
(3)
such that pply) llog 962+1 (v) 2 Ep(y) [log gor (y)). Where qos (zly) represents the approxi- mate posterior under the current prior oz. Thus, this update ensures a strict improvement in the expected log-evidence. We present detailed proof in the Appendix.
As established in optimizing the prior using the objective in Eqn. ensures that each update step systematically refines the prior toward a more faithful approximation of the underlying data
distribution. Specifically, 9dz+1 (I) is more consistent with the distribution of observations p(v)
than go (z). The update of the prior parameters Øk+1 follows a two-stage procedure: first, samples drawn from the posterior distribution qo, (aly); next, the prior model To (x)) is trained to
approximate this posterior by fitting to the generated samples. A central challenge in this framework the accurate sampling from the posterior distribution qø,, (arly), particularly during the early stages of active discovery when observations are inherently sparse. This data scarcity significantly limits the efficacy of traditional data-driven optimization approaches. Moreover, the challenge is intensified by the fact that repeated updates (k > 1) are both computationally and time-demanding. Consequently, it is imperative to design prior model that is both swiftly adaptable to limited observation and lightweight in complexity. Large-scale diffusion models, while powerful, are typically data-intensive and ill ill-suited for such low-resource settings. Our objective is to develop model that can efficiently adapt under constrained data regimes without compromising the quality of posterior approximation.
Swiftly Adaptable Prior model with Limited Observation To address this challenge, we draw inspiration from Doob's 's h-traanform, which enables sampling conditioned on the observations gathered. This perspective offers a powerful lens through which we construct an adaptive mechanism capable of efficiently guiding the prior with minimal data. Specifically, conditional sampling from the posterior distribution go. (xlyy) requires access to the posterior score Vz log pe Y v). conditioned given observation y. Since diffusion models are trained to approximate the score function of the marginal data distribution, i.e., s ~ V lo lo be adapted for conditional inference by applying Bayes' theorem: -Y=
(z)),
) a pre-trained diffusion model can
V x log Pe (z) Y = y) s sf V lY
The term Vz lo y x) is commonly referred to as the guidance term, as it effectively steers the reverse diffusion process toward samples consistent with the observation y. However, computing this guidance term is generally analytically intractable, which poses a significant challenge in performing conditional generation. Before delving into how Doob's h--transform can be harnessed to efficiently approximate the conditional guidance term, especially data-scarce regimes, we first introduce the formal definition of Doob's 's h-transform. This foundational understanding will later enable us to leverage its powerful structure for efficient and adaptive conditional sampling.
Definition 1 (Doob's s h-transform).
S Consider the following unconditional reverse-time SDE with fe as the drift and as the diffusion coefficient.
dx, = (Xt(),) - of xx, (X.) dt + a,dWe, XT Pp~
The corresponding conditional process (X, Xo E B) evolves according to the SDE:
d.., = (H.. o
of VH. (Xo E B H:) dt + or,W, HT ~ Pr ~ N 1) (5)
where the backward drift be(HH) is defined as; by (He) f((H)) V H. Inp:(H.) and the conditional law satisfies Law 11;) = 1 21,00 To B) with P(Xo E 1 We denote the conditional process as He and the corresponding unconditional process as Xt. Doob's 's h-transform illustrates that conditioning a diffusion process reach target set Xo E B at terminal time T yields a new diffusion process governed by an adjusted drift term (as shown in blue ). This conditional process is guaranteed to reach the desired event within a finite time T. The function lo(t, Hy) 2 boj (Xo B Hi) is known as the h-transform.

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Dhighigh highlighhs the current step. hinges on the interplay between the unconditional score and conditional score term, which is solely characterized by Doob's 's h-transform. Consequently, comparing Equation 5 the posterior score can formulated as:
Definition
key insight: conditional sampling, informed by the observations collected up
V pi v) PM
V pt = =
(6)
Permanent Memory
y): Transient Memory
As shown in Equation 6 the posterior score naturally decomposes into two complementary com- ponents. The first term, derived from pretrained diffusion model, serves as a form of permanent encapry-encassulating broad, generalizable patterns acquired from large-scale training data. While this offers strong prior, it alone is insufficient in setting, where access domain-specific prior samples is available. To address this limitation, we introduce the second term as a transiens memory that modulates the pretrained dynamics in response to the limited observations collected during the active discovery process. This adaptive correction is governed by Doob's /a-transform, parameterized by allowing the model to align with newly encountered observations in the data. In the Appendix, we provide an interpretation that frames the h-transform as a correction mechanism for the unconditional score, offering insights into how it adapts the pretrained dynamics the conditional setting. Next, we detail how Ç can be efficiently learned to enable rapid adaptation in data-scarce scenarios. Interestingly, the parameter can be optimized using an approach analogous to denoising score matching, as formalized in the following Lemma.
Lemma 1. Consider the following stochastic differential equation for the conditional process:
dH, [f((H)) of (V H, (o + he(H:))) dt + a.dW,, where Hr of (p(oo I w)] [0]=1 J priox | 2o) p(zu v) dæy. The h-transform function h; admits denoising score-matching representation: hū arg minn,eH LDSM (be), where
(Dsm = EE
(H)) + H. (n)) - VH In In (H, Xo)
Xarp(zzul))
(mo)
The proof is in the Appendix. Based on this Lemma, we optimize Ç as follows:
|| (1) o. (H.)) - =|]
min Exxor c
Let Hr = Va Xo + VI- where (Xo, ~ (5 y) and e ~ NO, I). The function A denotes a neural network designed to approximate the h-traanform. Crucially, the loss function in Equation 7 operates exclusively through forward evaluations of the pre-trained model and does not necessitate backpropagation through the fixed parameters 6*. Consequently, the h--transform is tasked solely with learning the residual noise component, effectively serving as a corrective mechanism. This design choice permits the h-model to remain lightweight and shallow, thereby enabling rapid adaptation even in regimes with extremely limited observations. Following each observation, we draw posterior samples Xo (0 y) using the posterior score composed of the frozen primary memory of (x) and the transient memory h (x. y). These samples are then used to update the transient memory parameters Ç via the objective 7 thereby ensuring that the resulting prior & c-consisting of both 8 and the updated ç-yields a strict improvement in the expected log-evidence, as formalized in Formally, the following theorem establishes that updating the transient memory parameter according to leads to a monotonic improvement of the composite prior Φ ()
Theorem 1. Let Φ -0, Q) denote the parameters of the prior, where 0 corresponds to a fixed pre-trained model and Ç parameterizes the learnable h-trrasffrm module. Suppose Ç is updated according Equation 7 yielding an updated parameter Gre and an updated prior Onew (f) (new) Then, the marginal expected log-evidence satisfies the following:
Ep(g) 9om.. (v)] 2 Ep(w) [log (3)).
We present detailed proof in the Appendix. Next, we present our methodology for updating the h-model, designed to enable seamless adaptation of the reverse diffusion dynamics.
5

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Learning Dynamics of h-model A natural strategy is to iteratively update the h-model after each new observation, thereby refining the prior and leveraging this improved prior to guide subsequent rounds of ATD more effectively. However, in the early stages of the discovery process, the available observations are often too sparse to capture the structure of the underlying search space. Updating the h-model solely based on such limited data can lead to premature convergence to suboptimal regions in the parameter space, from which recovery becomes increasingly difficult-even as more search progresses. This challenge is further intensified by
data becomes available gradually the ht-model's intended adaptability, as rapid updates may amplify the risk of overfitting to early, uninformative sig- nals. To validate this hypothesis, we conducted a toy experiment (illustrated in Fig. 2). comparing two strate- gies for updating the h-model. In the first, the h-model updated after every observation; in the second, updates occur only after accumulating several observations. We visualize the resulting posterior samples at different stages. When the h-model is updated after each individual obser- vation, the posterior becomes noticeably noisy during the early phase of discovery, likely due to limited data. In contrast, postponing the updates results in more stable and coherent posterior samples that better reflect the gathered observations, enabling the diffusion process to incorporate new information more effectively at each stage. Motivated by this observation, we introduce a simple yet effective scheduling strategy for updating the h-model. The proposed scheduler (detailed in Appendix) adapts dynamically with the query budget-startingg starting with infrequent updates and increasing in frequency as the search progresses. This design leverages the fact that updates become more reliable over time due to the increasing accumulation of informative observations.
Figure 2: h-model adaptability dynamics. We use Diffusion model trained MNIST as permanent memory (16 samples per Fig).
Theorem 2.
Let di (0. (e) be the prior parameters at observation step t. Suppose Çe is 7 yielding Φi+* = (0, (++x) after l additional observations.
updated following Equation Then the expected log-evidence improves monotonically:
)ppee+>) to. (ile-(()) (v)] 2 Eppee (log 2o, (v)]-
where yr++ represents the set of observations gathered uptill time t + k; and k 2 1.
We present detailed proof in the Appendix. Next, we introduce a sampling strategy that capitalizes on the updated prior developed thus far, guiding effective and budget-conscious ATD.
Sampling Strategy for ATD Utilizing the Updated Prior An effective sampling strategy that strikes the right balance between exploration and exploitation is crucial for solving ATD. We first describe how we approach the exploration using the observations collected thus far. To achieve this, we adopt a maximum-entropy strategy, selecting the measurement qt at the t-th query step as
exp arg max (+ 1(- arg - Rs (log p( v()))
le
qr
Here, H represents entropy, ât denotes samples from the approximate posterior qox-, (x yt- 1). Note that we utilize the final updated prior Φ = (0, (--1) to sample from the posterior. Qt represents the set of locations queried up to time I, and y/-1 represents the set of observations up to time / - 1. As defined in Equation 8 we select the query location that corresponds to the maximum entropy.
To compute log p( / Qt, 11- we begin by drawing P samples from the posterior q (z yt-1). denoting the i-th sample as 2t. We then approximate log p( Q+,, yt-1) using a mixture of Gaussians:
p( Qt. Mt-1) 1)- = Ei= (á I.. In the following Theorem, we derive a result that allows us to compute gt utilizing the expression of p( 1t-
Theorem 3. Assuming l represents the set of possible measurement locations at step 1, and that all samples from the posterior T
(x) 1t-11) have equal weights (o:; = =Oj, Vi,j), then,
P
P
(Emex(la)
(" In. -10( 1oc)
d. = arg max
Σ
log
exp
20
3=
where lgg. selects element (.) indexed by qu- Detailed proof is in the Appendix.

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The implication is that the optimal next observation location (o.") lies in the region of the search space where the predicted semantics (o(") show the highest disagreement among the posterior samples (i E O,.... P). This disagreement is quantified by a metric, denoted as exple ( (q:). which enables us to rank candidate observation locations and thereby guide exploration more effectively.
In scenarios where the observation space is composed of pixels, each a, represents a full image conditioned on the observed pixels yt-1-
P
(0) (LE
expl scoro (0:)
(9)
2
==
We now describe how the collected observations are used to guide effective exploitation. Specifically, we: (i) employ a reward model (rn)). parameterized by 1) and incrementally trained on supervised data gathered from observations, to predict whether an observed location corresponds to the target of interest; and (ii) estimate the expected log- liiklihhodd score at a location qt. denoted as likeli (q:). defined as Eg, [log p(tz Qt, 1))a) This score is key to prioritizing locations during exploitation. The following proposition provides a closed-form expression for computing likeli (gr).
Proposition 2. The expected log- ligeliielihood score at qt. can be expressed as follows:
P
((0)))
14 [xt 1n.)
likeligore (g() =
exp
20
1= f=0
The derivation of Proposition is provided in Appendix. The term likelig (qt) plays a central role in computing the exploitation score at measurement location qt, Specifically, the exploitation score, score exploit (o.n) (gt), is defined as the swward-wiighte expected log- log-likelihood, as shown below:
exploit(@..) (2:) likeli (2:)
(n(( Ja.)
(10)
Expected log. log-likellhood
reward
As per Eqn. 10, a measurement location q is favored for exploitation it meets two criteria: (1) the predicted content qu is highly likely to correspond to the target of interest, indicated by the reward model (ra);; and (2) the estimated content at gr. denoted as [=](1] I1 exhibit strong agreement across the posterior samples, suggesting high predictability about the content at that location. Note that the reward model parameters (17) are randomly initialized and progressively updated using binary cross-entropy loss as new supervised data becomes available after each observation. While the reward model is initially mnrefined-resulting in less reliable exploitation scores-the is not a limitation, as sampling strategy is designed to emphasize exploration during the early stages of the discovery process. We now bring together the core components to formulate the proposed sampling strategy for efficient active target discovery. At each time step t. potential measurement locations (qt) are ranked by jointly considering both exploration and exploitation scores, as below:
Score (g.) = a(B) exple (g.) + (1 aaBB) exploit score (q:)
(11)
Here, (BB is a budget-dependent function that enables a dynamic and adaptive balance between exploration and exploitation. After computing the combined score for each candidate location ge (as defined in Eqn. II), the location with the highest score is selected for sampling. The choice of (BB) is problem-specifi and can be tailored accordingly. A straightforward and effective option is to define it as linear function of the remaining budget, such as aBB) = B-t We empirically show that this simple formulation performs well across diverse application domains. The complete training and sampling algorithm is detailed in the Appendix, with a visual overview provided in the Appendix. Finally, we demonstrate that the improvement of the prior ó in turn leads increasingly accurate estimates of the score defined in Equation [1 as formally stated in Theorem
Theorem 4. Let & and dhew denote the prior parameters before and after updating the h-model using the objective in Equation (7). Then the following relation holds,
||Score (o mr (9t)) Score (2:) 2 ||Score ,r)( (x
(o...) (q:)l
Here, Score my) ,²) (9)) represents the true score estimate computed using the optimal prior 8' and optimal reward model 11", and î denotes the updated reward model parameter.
7

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We present the proof in the Appendix. When tackling consecutive tasks from the same domain, we update the long-term memory using posterior samples gathered the end of each discovery process. promoting faster and more efficient adaptation to subsequent tasks. We present pictorial illustration of our proposed EM-PTDM approach in Figure Next, we present our detailed experimental results
Active Target Discovery Task
Step
Step
Step
Step 350
Target
Decide Where to Query the Next Step
Pro- Trined Diftusion
Training Messurements
Onine Feedback Reward Neural Network
Update with Partial Oiservattons
Decision Making Score
Posteriors
Entropy
Likelihood
Figure 3: An Overview of EM-PTDM Framework.
validate the efficacy of our proposed method.
Empirical Analysis
Evaluation metrics. Since ATD seeks maximize the identification of measurement locations containing the target of interest, we assess performance using the success rate (SR) of selecting mea- surement locations that belong to the target during exploration in partially observable environments. Therefore, SR is defined as: SR = Σ min (B.U.) Σt= vi ( where, = number tasks. Here, Ug denotes the maximum number of measurement locations containing the target in the i-th search task. We evaluate EM-PTDM and the baselines across different measurement budgets B {150, 200, 250, 300, 350) for various target categories and application domains.
Baselines. We compare our proposed EM-PTDM policy to the following baselines:
Random Search (RS), in which unexplored measurement locations are selected uniformly at random.
DiffATD 1 leverages a pre-trained diffusion model guide sampling based on partially observed data, efficiently discovering target regions within fixed budget.
(GA) selects ge with the highest exploit (e.n) (q:) among unexplored locations and updates reward model ry via binary cross cross-entreee coos-enttoppy after each observation.
score
Active Discovery of Unknown Species from Known Species Distribution We begin our evalua- tion EM-PTDM in setting where the permanent memory trained to approximate the distribution of species from iNaturalist [3). The distribution is formed by dividing large geospatial region into equal-sized grids and counting target species occurrences on each grid, as detailed in Appendix. The goal is to actively discover Coccinella Septempunctata (CS) under a strict sampling budget using prior trained on the distribution of Gladicosa and Gonioctena (GG). The results presented Table []] suggest that EM-PTDM significantly outperforms the baseline in terms of SR, highlighting the capa- bility the proposed framework ATD under an uninformative prior. We further visualize (in 4) how EM-PTDM, starting from uninformative prior, rapidly approximates the true distribution with only a few observations, demonstrating its swift adaptability and efficiency in data-scarce scenarios.

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Prior
Step -0
Step - 150
Step 250
Target DistrBution
Table 1: SR Comparison with Baselines.
DifAATD
Active Discovery of CS Species with Species GG as Prior.
Mothod
B 150
B 200
B 250
EM PIDM
RS
0.1624
0.2327
0.2775
DIEATD
0.3420
0.4365
0.4808
GA
0,4061
0.5067
0.5567
EM-PTDM
0,4983
0.6495
0.6989
Figure 4: Active Discovery of CS species.
Active Discovery of Unknown Overhead Objects from Ground-vied view Prior We further assess EM-PTDM in a challenging cross-view view setting, where the task is to actively discover novel objects from DOTA overhead imagery [6) leveraging an uninformative prior learned solely from ground-level images of semantically disjoint classes from Imagenet 77. The results are presented in Table [ We observe that EM-PTDM consistently outperforms the baseline, with the performance gap widening as the search budget increases, highlighting the strength of its cumulatively refined prior in driving efficient exploration and informed target discovery. Additionally, dynamics of EM-PTDM and DiffATD at two stages of the active discovery process. As shown in Figure 5 while both models initially struggle due to uninformative priors, EM-PTDM rapidly adapts through Doob's 's h-transform, enabling more efficient target discovery as observations accumulate.
compare the exploration
Step
Step
Target
Table 2: SR Comparison with Baselines.
DMATD
Active Discovery of Overhead Objects with ImageNet as Prior.
Method
8 250
B
300
B
350
FM-PTMM
RS
0.2325
0,2852
0.3207
DITATD
0,5143
0.6391
0.7348
0,4784
0.5659
0.6562
Figure 5: Active Discovery of Overhead objects.
EM-PTDM
0.5620
0.7013
0.8256
Enhancing Permanent Memory with Domain Cues for Improved In-Domain Target Discovery In real-world settings, it's common to encounter scenarios where ATD tasks must be addressed consecutively within similar domains, requiring models that can retain and transfer knowledge effectively. To support efficient adaptation in sequential ATD tasks within the same domain, we update the permanent memory speeiiri-peeiiicllll.... the pretrained diffusion model (s > posterior samples generated at the final step of the previous task, conditioned on all collected observations.
This update allows the permanent memory to gain domain-specific structural knowledge, thereby reducing the divergence between prior and posterior distributions in subsequent tasks. As a result, the learning task of doob's h-model becomes easier as the correction needed for rapid adaptation diminishes, enabling the model explore and discover new targets more effectively with fewer observations. We assess the impact of updating permanent memory after each task by compar- ing it against a static-memrry baseline. For this comparison, we consider the task of ATD of overhead objects with ImageNet as the prior. As reported in 3 the results reveal a marked improvement in the SR when updates are applied, underscoring the value of accumulating domain-specific knowledge in permanent memory to accelerate adaptation and enhance target discovery in related tasks.
Table 3: Effect of Permanent Memory
ATD Overhead Objects with ImageNet as Prior.
update
8 250
1
300
B 350
No Yes
0.5620
0,7013
0.8256
0,5839
0.7194
0.8461
The Role of Transient Memory in Rapid Adaptation to Novel ATD Tasks To assess the impact of transient memory, we compare posterior estimates generated with and without the proposed transient memory mechanism, starting from an uninformative prior. As illustrated in Fig. 7 incorporating transient memory via the h-model enables rapid adaptation from sparse early observations, resulting in posterior estimates that closely approximate the ground truth and facilitate more efficient target discovery. In contrast, the baseline, which relies solely on permanent memory, yields an incorrect posterior, resulting in limited exploration capability in early stages, underscoring the critical role of the h-model in accelerating effective exploration. We quantitatively assess the role of the h-model by measuring L2 distance- based semantic dissimilarity between the posterior and ground-truth targets. Results 6 show that incorporating the h-model significantly accelerates convergence to the true posterior, as dissimilarity drops much faster compared to using the permanent memory alone, demonstrating the h-moldl's 's effectiveness in rapidly correcting the prior with minimal observations.

---

Figure 7: Posterior Dynamics with and without h-model.
Only Fermanert Nenwey
Tagg
60
EM-PIDM
Saxplo
Dieans foom
10
20
Wibh Traniird Mersry
8 10 H Biioodel Updote Step (every 20 mesurrmeen steps)
Swrple
Figure 6: Effectiveness of Transient Memory.
An Important Observation: ATD is not just About Reconstruction One might ask: if the primary goal is for the posterior samples to accurately reconstruct the search space, isn't that sufficient for efficient target discovery? Interestingly, in our setting, a precise reconstruction of the entire search space is not strictly necessary, as long as the model effectively identifies and reconstructs the target regions, efficient discovery can still be achieved. To validate this hypothesis, we conduct an experiment and visualize the posterior intermediate stages of active target discovery. We compare posterior samples from EM-PTDM and DifFATD using a representative task where EM- PTDM significantly outperforms DiffATD, allowing us to understand how the posterior contributes to improved target discovery. We present the visualization in the Figure g Our observations reveal that, while EM-PTDM's posterior samples exhibit lower overall reconstruction quality compared to those from DiSTATD, they more effectively focus target-rich regions (For example, the highlighted Red box in the Figure 8), leading to significantly improved target discovery performance. This highlights& a key insight: successful target discovery relies more on accurately modeling the regions of interest than on reconstructing the entire search space.
DifFATD Posterior Intermediate
EM-PTDM Posterior at Intermediate Active Target Discovery Phase
Ground Truth Posterior
Active Target Discovery Phase
Figure 8: ATD is about Discovering Targets, NOT just Reconstructing the Search Space.
5 Related Work
10 have been developed for ATD; however, they typically assume full observability of the search space and require access to large-scale, pre-labeled datasets to learn efficient exploration strategies. Training-free approaches inspired by Bayesian decision the- offer an appealing alternative, yet their dependence on complete observability limits their effectiveness in partially observable settings. More recently, a new class of methods [15] 17 has emerged, explicitly addressing active discovery under partial observability. Nevertheless, these approaches still face major challenge challenge-their their heavy reliance on extensive annotated datasets to reach optimal performance. DifFATD (I] advances active target discovery by enabling efficient exploration in partially observable environment without requiring task-specifie labeled data. However, it still depends on domain- specific prior samples to learn an effective prior model, limiting its applicability in domains where such data is unavailable. To address this critical gap, we propose EM-PTDM, novel framework that enables active target discovery without relying on any prior domain samples.
Several RL-based methods 8
ory [2 B 14
Conclusion
We propose EM-PTDM, a principled and generalizable framework for ATD in partially observable environments, remarkably operating without any task-specifi prior data, significantly broadening its applicability in diverse domains. EM-PTDM bridges solid theoretical foundations with compelling empirical performance across diverse domains, ranging from rare species discovery to remote sensing.
10

---

This research was partially supported by the National Science Foundation (CCF-2403758, IIS-2214141), Army Research Office (W911NF2510059), Office of Naval Research (N000142412663), and Amazon.
Ackmowledgement
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Appendix: Active Target Discovery under Uninformative Prior: The Power of Permanent and Transient Memory
Overview of the Contents
A: Proofs of Theoretical Results
A.1 Proof of Proposition
21
A.2 Proof of Lemma 1
21
A.3 Proof of Theorem
22
A.4 Proof Theorem 2
22
A.5 Proof Theorem 3
23
A.6 Proof of Theorem 4
24-25
A.7 Proof of Proposition 2
25-26
B: Empirical Analysis of h model
26
B.I Doob's h-transform as the Correction Factor
26
B.2 Details of h-model Update Scheduler
26-27
B.3 Effect of h-model Update Scheduler
27
C: Exploratory Nature of EM-PTDM
27
D: Training and Inference Pseudocode
27-28
E: Efficacy of h-model In Estimating The Search Space With Only Few Observations
29
F: Analyzing the Role of Permanent and Transient Memory for Enhancing In-Domain
29
Target Discovery
G: Effect of k(3)
29-30
H: EM-PTDM's Capability Discovering Isolated Targets within Observation Budget
30-31
Species Distribution Modelling as Active Target Discovery Problem
J: Additional Results on Active Discovery of Unknown Species from Known Species
31-32
Distribution
K: More Visualizations on Efficiency of h-model's Adaptability From Very Sparse
32-33
Observations
L: More Visualizations of the Exploration Behavior of EM-PTDM at Different Active
33-34
Target Discovery Phases
M: Active Target Discovery of Balls Using MNIST Images as the Prior
35
M.1 Dataset Creation Procedure
35
M.2 SR Comparisons with Baseline Approaches
35
M.3 Analyzing the Exploration Strategies of EM-PTDM and DifFATD Under Increasing
35-36
Task Complexity
N: Architecture, Training Details: h-model, Pretrained Diffusion Model, and the
36
Reward Model; and Computing Resources
N.1 Details h-model
36
N.2 Details Reward Model
36-37
N.3 Details Primary Memory as Pretrained Diffusion Model
36-37
O: Statistical Significance Results of EM-PTDM
37-38
P: Impact of Weak Permanent Memory on Active Target Discovery Performance
38
Q: More Details on Computational Cost across Search Space
38
R: Code Link
39
20

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A Proofs of Theoretical Results
A.1
Proof of Proposition 1
Proof.
0" = arg max Ep(n) [log [o)] 0
(12)
arg min KL (p(v) ll go())
(13)
The core principle the EM algorithm that, for any two parameter sets 0, and 0s, the following identity holds:
qe (v)
log 98, (x, v)
46 (x y)
log
(14)
qo: (1)
qo, (xr,) v)
qu, (3r y)
log qo (2t, y)
E go, (=|p)
+ KL (go, (ar w) go (x v))
(15)
qo, (1r, v)
2 Egg (=ls) [log 4o. (or, y) log qo, (Ir, y)]
(16)
This inequality remains valid when taking the expectation over p(y). Consequently, starting from an initial parameter setting Co. the EM update rule can be expressed as:
0k+1 arg max Ep( (rll) [log qo (z, y) - log qo, (x. y)]
(17)
arg max (e Deg (mle) [log qa (3z, y)]
(18)
In the empirical Bayes setting, the forward model ply ax) known and only the parameters of the prior (x(x) should be optimized. In this case, Eq. 18 becomes:
0x+1 = arg max Ee, (xlv) [log go (x) + p(y x)]
(19)
11
ak+1 arg max BB (alv) [log (x))
(20)
A.2 Proof of Lemma
Proof. We can express the conditional score follows:
Z3, Inp:(x 1 v) = Va, In F (ar ao) of | |et v) da
(21)
The minimizer is obtained by exploiting the property that the conditional expectation yields the optimal solution under the mean squared error criterion:
H. In (He Xo) Vn, (H,) = y. He = x.]
(22)
(2 y)
V In Pejo mo) V. Inp( ( H: = x, Y y) dro
(23)
v In Pejo(1 æv) pojr
H. x, y) dry V. (x))
(24)
In v) In = V. xx)
(25)
(26)
21

---

A.3
Proof of Theorem
Proof.
arg max I p(u) log [b))
(27)
Utilizing the result of Theorem can express the above expression as follows:
doow arg max Ep(y) (xlv) [log qs (z)]
(28)
Maximizing the above objective involves computing v log (z). Following the approach in denoising score matching, the above optimization can be equivalently reformulated as:
Çoow min E (Xo. ),, 1 ( Y) + of (x+) -
(29)
Let vt = Von Xo + v1 or e, where Xn ~ (0( y). Y ~ and e ~ (),, Also, deo = (0", (mou)
Thus, optimizing the objective in Equation 29 is equivalent to one step of EM. Hence, guarantees the improvement of expected log-evidence. As result, can write:
Ep(s) [og Ya (v)) 2 Ep(y) [log go (v))
A.4 Proof of Theorem 2
Proof.
E Ep(geta) [log goesk (y)
(30)
Assuming the observations collected during the active discovery process are independent, we can decompose the above expression into two parts as follows:
Ep(v.) [log 9orts (y)) x Eponreaen n) Dog go.t4 (v)
(31)
part!
part2
The set of observations gathered from time step t + is denoted as 1r+R:(t+1)- For Partl, we can write,
Ep(v.) [log Lo (v)) 2 Expr (log yo, (v)) (Following Theorem 2)
(32)
For Part2, we can write,
Ep(re [log Touis (v)) 2 Beleeeeeee [log do, (v)) (By Definition)
(33)
The above relation holds because, unlike 61. the model Φ is trained on posterior samples explicitly conditioned on the observations Vt++:(t++1-- As result, when di+x optimally trained, the left-hand side of Equation 33 reaches its optimal value. In contrast, since Φa is never exposed to 11+k:(0+1) during training, it cannot attain the optimal value of the left-hand side in Equation 33
Finally, combining the results of Equation 32 and 33 we can write:
Epig-=)) [log ao. (v) E Ep(w [log qo, (v)
22

---

A.5
Proof of Theorem 3
Proof. We start with the definition of ca as follows:
9t arg max Es, [logp(5 (8:(Q(: where pltz|Qts y Σ
oi o2
q5
According to 18)
| -06²"11
112
9:
log
ayexp
20
k 0
We can write,
|1 . 113
exp arg max
at log
ajexp
20
1=0
i=0
|
(1) (8)
112)
4t
CP arg max
log
exp
(By assuming. a; Ojj Vi,j)
20
Enco, (1a1 -12 1a)2
1.)
qt
cpp = arg max
log
EXp
20
1
We decompose into two parts: one representing the set of potential measurement locations the query step I, and the other corresponding to the set of locations already selected in Qt-1- Hence, we can express it as follows:
EmExn(E("1a - -10 ",E,,,,,(E""" [+]
4: arg max
log
exp
20
1.
(La (1)
)
03
exp arg max
log
II exp
91
10
II
exp
20
20
rEQu-1
(11 17t
[1 lgc )2
([a.0)
(4) r
Σ
arg max
16
202
202
91 Ek
We can ignore as it docsa't 't depend on choice of measurement location time 1.
(1x
[5]
[3(10)11] )m.
arg max
gt
20
1.
QEEk
P
Σ EmER (1o!20)
1g.
41
exp
arg max
log
exp
20
1=0
1=0
23

---

A.6 Proof of Theorem 4
Proof. Using Equation 12, we can decompose the score follows:
(r) (core(a.)) (4t) - a(B) (exple. (4e) - exple (9t))
+ (1 a(B)) (exploit soore score .y ()-)))) ((t) (r)(())
- exploit score (o.n) ((.))
(34)
By following a similar decomposition, we can write,
[Score ( Score (then (g:)ll aBB)) (expl
score (ge) expl Phac
(Rt)
+ (1 - (B)) (exploit(s (d= .y (d- (9)) - exploit (phan (9t)
score
score
(35)
We write,
expl pooree (qt) exxploore (q:)
(explrore o
(gt) explate (qt)
soplsoore deev
(Follows from Proposition and Theorem 1)
(36)
The above relation holds Pnew is obtained by applying one iteration of EM, thus guaranteeing improvement from the previous iteration prior (ø). Hence, ensure a more accurate exploration score estimation compared to the prior of previous iteration.
Next, we will compare terms and and show that
(exploit (ør iy" (gc) exploit (4..)) (q.) 2 (exploit (0""") (g)) - exploit soore
(Brow (9))
Utilizing the expression in 11, we compare the exploit scores computed via different parameterizations of the prior as follows:
Score exploit(a.)) (at)
likeli (gt)
Th (1a Ime))
Expected log likelihood
reward
We can rewrite the above expression as follows:
( 1a.)1 exploit (d-n)) (4:) = likeli (4+) Beel") (18("/noota))) [ro(((b
score
Following exactly similar steps, we can also write
score exploit (camn (4:) = likelizooro fhex
sccoe
(4:) + E | (xlo)) (ra((s(()) In.
Following the same reasoning as in 37, we can write (likeligcore (q:) likeli (q:)) 2 (likeligoore (ge) likeliscore Pree
(Follows from Proposition 1 and Theorem 1)
(37)
Now, note that at the beginning of the active target discovery process, (,,((=!)) ((,()) ).
As Qnew is a improved parameterization of the previous iteration prior o, thus posterior samples from Jow. (x y) are more reliable and accurate compared to the posterior samples from ( y) and thus reward evaluated on posterior samples from &aw. (x y) are more reliable. Furthermore, the reward model ri benefits from training more diverse samples, entropy computed using the updated prior dnew more accurate than that from Φb This leads to improved data diversity during collection, enabling Ta to converge faster than Ty, The following lemma supports this hypothesis:

---

Lemma 2 (Diverse Data Improves Convergence). 20 Let 0, be the parameters of a neural network trained using SGD with batch size I and learning rate on dataset S. Let Ls be the empirical loss. Assume the loss is T-smooth and gradients are bounded by G. Let S and S2 be two datasets of size n, with (SS) > D(S2). Then, for the same number of iterations the expected generalization gap
B(C(0))) - -( < where, D(S)
Σ Ia z;ll for (2r, vi), (r (r),9;) E 6
n
where o and o are trained S1 and S2 respectively, assuming the data distribution D has high support over X.
Hence, o is closer to optimal solution of (()) than o7 in fewer steps, assuming same training budget.
Thus, utilizing the result of the lemma we can write:
[ 12 (oto)) In ((o) Jn.3] 16 (a5") | In (1= lx N
(IE [ (olo)))
[n ([a) (
lo.)l LE pa gog
(r=(1 (1) lec
(38)
Now, combining the results of (38) and (39), we can write
score (exploit
(0r m²) (gc) exploit score (6.1) (q:) 2 (exploit score
.n²) (gr) exploit score
(drew .)) (gc)
(39)
Finally, leveraging the results of (37) and (40), and utilizing the definition (35), we can write
[| mn) Score (9:)) 2 |Score (.',)))()))) - Score (bren (4t)l
A.7 Proof of Proposition 2
Proof. We start with the definition of entropy H:
Ex, [log p Qt,, Vr- 1/- 1)] = H ( (fz]Qt, 9t-1)
Following the results of [18]. and by setting a; = aj = 1, we obtain:
P
|| (1)
113
Es, ((e 10. 1)]
Σ
log
exp
20
1=U
f=U
EnEo (1x 1a - |2 (2
E,, ((t 91-13]
Σ
log
exp
20
i
Assuming & is the set of potential measurement locations at time step t, and Q: = Qt-1 U lt. where
4t.5 E k.
Emnea(laf b0
[=((0]] )2
ErEo,, -100 1,)2
Eg, (o:loo(((e)) 9--1 x
Σ log
exp
20
((a((0)
[+
(L (6)
(0 12
E,, [log 1l, 31 91-1)1 x Σ
log
II
exp
10
II
exp
202
2 x
i.j
rE 1EQL11
25

---

(L.)
(1) 99t
[
5 Ige
)
([o!"), 1r 1,]2
Es, p(0z Ve-1e-1) x
20
20
gEEk
We then compute the expected log-likelihood at specified measurement location dt. discarding all terms independent of qt- This key observation allows us to simplify the expression as follows:
(1) br
10e lec)
Es, ((o Qts 1/+
Σ Ad
20
The expected log-likelihood at messurement location q Equivalently, we can write the above expression
E2, [e.1logp(ee(Q22 p(t yt yt-
x
Σ Σ exp
(L.
(6) 10
[
(3)
10c
)22
20
likeltscore (gi)
By definition, the left-hand side the above expression corresponds to likeliscore (qt).
B Empirical Analysis of h model
B.1 Doob's h-transform as the Correction Factor
We demonstrate that the h-transformm serves correction term for Tweedie's estimate. Specifically, the conditional Tweedie estimate can be expressed as:
(1,, y) + sy (It)
It
ai
B Biz0
Ze,yl v] x @o v)
Vae
0
at log (x+,
Vot
CFt
Vau
Unconditional Tweedie estimate
Correction Factor (L.e., h-transform)
In Equation (40), the first term represents the unconditional Tweedie estimate, illustrating that the f--transform can be viewed as a correction to the unconditional denoised prediction.
B.2 Details of li-model Update Scheduler
As highlighted in the main paper, the pessimistic updating of the h-model parameters plays a critical role in stabilizing the prior model's adaptability dynamics. While straightforward heuristic might suggest updating the h-model after a fixed number observations, this approach only provides marginal improvements. A more effective scheduling strategy requires fewer updates during the early stages of discovery. allowing the model to gather ample data and avoid the risk of erroneous updates when the observations still sparse. However, the discovery process progresses and the model's understanding of the search space strengthens, more frequent updates of the h-model become essential. This shift enables more effective exploitation of the environment, the model has already gathered enough information, making the need for pessimistic updates unnecessary. Motivated by this observation, propose the following h-model update scheduler:
B
i
At:
(40)
U
26

---

Here, B denotes the overall sampling budget, U is the total number of h-model updates throughout the active discovery process, indicates the current sampling step. 7 governs the decay rate, and At, defines the interval between two successive updates of the h-model parameters at the i-th sampling step. Note that since 7 2 1, the update frequency the h-model naturally accelerates with increasing i, leading to more frequent updates during the later stages of the active discovery process.
B.3 Effect of h-model Update Scheduler
In this section, we evaluate the effectiveness of the h-model update scheduler by comparing two variants of EEM-PTD: one using a uniform update schedule and the other employing the adaptive scheduler defined in Equation 40 For the uniform scheduler, the h-model is updated
fixed every 20 update steps. For the adaptive scheduler, we set = 1, U = 30, and an observation budget of B = {200, 250}. The comparative results under this configuration are For this analysis, we consider active discovery of balls with diffusion model trained on MNIST data as the prior model. Our empirical results show that EM-PTDM with an adaptive h-model update scheduler consistently outperforms its uniform counterpart across various measurement budgets. This improvement can be attributed fewer updates in the early stages, allowing the model to collect more informative observations before updating and thus reducing the risk of premature or noisy updates. As the discovery progresses and the model gains a stronger understanding of the search space, the increased update frequency of h-model in later stages proves beneficial for accelcrating active target discovery.
antervals-specifiii
presented in Table 4
Table 4: Effect of Adaptive h-model Update Scheduler.
Active Discovery of Balls with MNIST Digit Images the Prior.
m-model update Schedule
B 200
B 250
Uniform
0.6856 0.7364
0.7875
Adaptive
0.8268
C Exploratory Nature of EM-PTDM
In active target discovery under an uninformative prior, exploration isn't just helpful-itts essential. Especially in the early stages, when the permanent memory offers little insight into the target domain and the correction factor is large, the /t-oddel must rapidly adapt. This demands smart, strategic exploration of the search space to collect informative observations, enabling the h-model to efficiently learn and calibrate the correction factor. To assess EM-PTDM's exploratory behavior, we tackle active target discovery of overhead objects using ground-level imagery as prior knowledge, evaluating across a wide range of observation budgets-from very sparse (200) to less sparse (350)-and benchmark against baseline methods. We present the results in the following Table 5
Table 5: Importance of Exploration
ATD of Overhead Objects with ImageNet as Prior.
Method
B 200
B 250
B 300
B 350
DiffATD
0.3873
0.5143
0.6391
0.7348
GA
0.3479
0.4784
0.5659
0.6562
EM-PTDM
0.4127
0.5620
0.7013
0.8256
We observe that EM-PTDM's performance improvement over baselines grows with the observation budget. When the budget low, the performance gap narrow, reflecting limited opportunity for exploration. As the budget increases, EM-PTDM leverages richer exploration to adapt its h-model, leading to significantly more effective target discovery.
D Training and Inference Pseudocode
Below present the training and inference pseudocode.
27

---

Algorithm 1 EM-PTDM SAMPLING STRATEGY (AT THE 1-TH OBSERVATION STEP)
Require: Current State of Transient Memory: Trained h-transform h (x. &o v) with parameters Ç.
Require: Permanent Memory as Unconditionally trained noise predictor sf" (x+)
Require: Noise schedule 3r ((), a₂ a(t)
Require: Sampling schedule a; = (1)
Require: Observation y, Posterior samples list ps = O. Success R = 0.
1: 2T Pr. (0,
Sample starting point
2: for P do
3: f -0
4: for / in (T, -1T--1.-... 10,-1,,.. 1,..., 1) do
5:
Ea +- ot (xt)
Predict unconditional noise
20 + It vV arÊa
6:
Vot
7:
&c x 15(1,, 80. v)
Predict correction noise via h-transform Estimate posterior noise
8:
E Eg E
9:
if then
10:
Sample ex P Pooise
else
12:
+ 0
end
+ V ā,-1 ofe ofEt Ftt VI āgē
14:
1t-1 f vāL-1
15:
ift |then
16:
8' ----1- end if end for ps.append(
18:
19:
20:
end for
Utilize Posterior samples in ps compute expl (q:) and exploit (g:) using Eqn. and 10 respectively for each E k. Compute scorc(q:) using Eqn.
11 for each d and sample a location d with the highest
scorc.
B B+ B [k} < {k} 9t
24: Update: Q, + Q--1 U 9t Vt + 9t-1 U [x]pr-
25: Update: D, < D,-1 U {[r]a y( R += y(u+
26: Train Tn with updated D, and optimize with Cross-Entropy loss.
27: return R
Algorithm 2 H-TRANNFORM FINE-TUNING (AT THE 2-TH OBSERVATION STEP)
Require: Posterior Samples drawn from qo.., (x 9t-1)
Require: Noise schedule 3, (t),, 0₂ = ā(t)
Require: Permanent Memory (i.e. Pre- Pre-Trained Noise predictor function) sf (z) with parameters 6*.
Require: Current state of Transient Memory (i.e. f--transform) 1y (xx, &o, y) with parameters Ç.
1: repeat
2: To Po 9d._, (x y(-1)
3: t~ Uniform {1, (I....,T) T})
4:
Er I)
Sample noise
5:
It - Varto + VT 14
6:
Eg + o (IA)
Estimate noise with pretrained model
in --vi-oree
7:
Vas
8:
&C h5 2o. 8)
Estimate correction via h-transform
9:
Take gradient descent step w.r.t. on
VeLlEe, Eo + ε
L is defined in Equation
11:
until convergence or maximum epochs reached return Updated h model Parameter Ç.
28

---

E
Efficacy of h-model in Estimating The Search Space with only Few Observations
We analyze the adaptability of the h-model using quantitative visualizations in the context of an active target discovery overhead objects, where ground-level ImageNet images serve as the prior. Specifically, assess the ht-mdell's role by computing L2-based semantic similarity between predicted and ground-truth targets (right 9b), and between predicted and ground-truth posteriors Paj. As depicted in Figure the inclusion of the ht-odel leads to significantly faster convergence to the true posterior and the true targets, thus enabling more informed target discovery. The rapid drop in dissimilarity compared to using permanent memory alone highlights the h-model's ability to quickly correct the prior with minimal observations.
Disunee foon GT Puneste
& 8/8
EM-PTM
EM-PTDM
8
8 &
Destese
26
6
13 14
11 15
H-mode Upbite Skep (every masunmment supps)
H-model Updati Stup (every 20 messecmmnt sleps)
(a) Distance between predicted and ground- truth posterior.
(b) L. Distance between predicted and ground-
truth targets.
Figure Quantitative analysis of h-model's adaptability in Active Target Discovery.
F Analyzing the Role of Permanent and Transient Memory for Enhancing In-Domain Target Discovery
Since we've seen that inside the EM-PTDM framework, updating permanent memory with posteriors from prior in-domain ATD tasks boosts performance, it raises key question: do still need the h-model? To investigate, we turn DifFATD state-of-the-ar baseline that uses only permanent memory. To update the permanent memory of DifTATD, we apply the same continual memory update strategy as in EM-PTDM, incorporating accumulated posteriors after each task, to see how far performance can go without the la-model. For this comparison, we examine active target discovery of overhead objects using ground-level ImageNet images as prior knowledge. While updating only the permanent memory leads to improved discovery rates compared to DiffATD with fixed permanent memory across different observation budgets. clear and consistent performance gap remains when compared to EM-PTDM, particularly when EM-PTDM updates its permanent memory after each in in-domain ATD task. These results, summarized in Table highlight the added value of the h-model in driving more effective exploration and adaptation irrespective of whether permanent memory being updated or not.
Table 6: Importance of h-model with or without Permanent Memory (PM) Update
ATD of Overhead Objects with ImageNet as Prior.
Method
250
300
B 350
DifFATD
0.5143
0.6391
0.7348
DifFATD w/ PM Update
0.5294
0.6623
0.7589
EM-PTDM
0.5620
0.7013
0,8256
EM-PTDM w/ PM Update
0.5859
0.7194
0.8461
G Effect of (B)
We conduct experiments to assess the impact of x(B) on EM-PTDM's active discovery perfor- mance. Specifically, we investigate how amplifying the exploration weight, by setting x(B) max x(a B)} with a > 1, and enhancing the exploitation weight by setting < 1, influence the overall effectiveness of the approach. We report results for {0.2, 1, 1,5) in two settings: using
29

---

Table 7: Effect of k(BB
Performance across varying a with B = 250
Target
Prior
0.2
1.0
5.0
Balls
MNIST
0.7416
0.7875
0.9272
overhead objects as targets with ground-level images as the prior (first row), and discovering target balls using MNIST digit images as the prior (second row). The results are summarized in Table 7 The best performance is achieved with = 5, and the results suggest that higher values of a boosts performance, reinforeing the fact that exploration is key to success in active target discovery under an uninformative prior.
H EM-PTDM's Capability of Discovering Isolated Targets within Observation Budget
To evaluate EM-PTDM's ability to uncover disjoint target regions within a limited sampling budget, design series of controlled toy experiments. In each task, the goal is discover varying number of balls- colls-positioned differently and with different radii-using a diffusion model pretrained on MNIST digits as the permanent memory. We systematically increase task difficulty by varying the number of target balls from 5 to 10. Notably, tasks with more targets demand effective exploration of the search space successfully locate all disjoint regions within the budget constraints. We present comparative visualizations of the exploration behavior of EM-PTDM and DiffATD with an active discovery task involving uncovering target balls with MNIST Images as the prior, shown in Fig. 11 As the number of disjoint targets increases, making the task more challenging and exploration-inteniive., EM-PTDM consistently succeeds discovering most, if all, targets within the given budget. In contrast, the baseline (i.c., DifFATD) relying solely on permanent memory struggles as task complexity rises, as seen Plot [0] These visualizations clearly demonstrate EM-PTDM's superior exploration capabilities, which are crucial for efficient target discovery in settings with multiple disjoint targets.
1.0
EM-PTDM
Ratio of Targets Found
DiffATD
0.8
0.6
0.4
0.2
0.0
40
80
120
160
200
240
280
Measurement Step
Figure 10: Comparison of the Discovery Process: EM-PTDM DiffATD. In this experiment, evaluate the active discovery of 10 target balls using a diffusion model trained on MNIST images as the prior. As the search budget increases, EM-PTDM consistently uncovers more disjoint target balls, thanks to its inherently exploratory behavior. In contrast, DifFATD struggles to discover as many targets as it lacks the same efficiency as EM-PTDM in exploring the search space.
30

---

DifFATD
EM-PTDM
Target
Figure 11: Comparison between EM-PTDM and DiffATD's Discovery. Green patches correspond to successful target discovery, and Red Patches correspond to unsuccessful observations. In this example, the task is to discover the balls with MNIST images the prior. The exploratory behavior of EM-PTDD, contrast to DifTATD, is evident the visualization.
I Species Distribution Modelling as Active Target Discovery Problem
We constructed our species distribution experiment using observation data of the chosen species from iNaturalist. Center points were 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 x 480 km in size (roughly 5 degrees in both latitude and longitude). Each retained region was discretized into 64x64 grid, where the value each cell represents the number of observed species. To simulate the querying process, each 2x2 block of grid cells treated as query.
J Additional Results on Active Discovery of Unknown Species from Known Species Distribution
In the main paper, we explored active discovery of Coccinella septempunctata (CS) using the known species distribution of Gladicosa and Gonioctena (GG) as the prior. This section extends our analysis to different species from the iNaturalist dataset. Specifically, involves discovering Species Cedar Waxwing from the known distribution of Species clape- Chickadee. compares the exploration behavior of EM-PTDM and DiffATD at various stages of target discovery. As shown, EM- EM-PTDM- starting from the same prior as DiffATD progressively and efficiently adapts the prior toward the true target distribution with only few task-specific observations. In contrast, DifFATD, which relies solely on static permanent memory, struggles to approximate the ground-truth distribution within the given observation budget.
evaluate EM-PTDM
task that
Table SR Comparison with Baselines.
Active Discovery of Cedar Waxwing Species with Species Black-capped Chickadee Prior.
Method
B 150
200
B 250
DiffATD
0.2319
0.3309
0.4453
GA
0.2232
0.3098
0.3116
EM-PTDM
0.3079
0.3854
0.6347
We further compare the performance EM-PTDM against baseline methods using Success Rate (SR) as the evaluation metric, with results summarized in Table The task involves actively discovering Species Cedar Waxwing from the known distribution Species Black-capped Chickadee. Consistent with other experimental settings, EM-PTDM significantly outperforms all baselines across varying observation budgets. These results further highlight the effectiveness of EM-PTDM in tackling active target discovery under uninformative prior.
31

---

Prior
Step 80
Step 150
Step 250
Target Distribution
DifATD
EM-PTDM
Figure 12: Exploration Behavior of Different Approaches. We visualize the explored Regions at Different Active Target Discovery Phases. We consider the task of Active Discovery of the species Cedar Waxwing with known distribution of the species Black-capped Chickadee. EM-PTDM discovers most target regions (i.e., more accurately discovers the existence of the species Cedar Waxwing).
K More Visualizations on Efficiency of h-model's Adaptability From Very Sparse Observations
In this section, we provide additional visualizations of posterior samples generated by EM-PTDM and DiffATD across different stages of active target discovery. As shown in Figures LB 14
L5}.
EM-PTDM produces samples that are more semantically aligned with the ground-truth posterior compared to DiffATD. Notably, even with sparse observations, EM-PTDM effectively simulates the search space, enabling more informed exploration and leading improved target discovery under an uninformative prior.
Only Permanent Memory
Target
Sample
Estimate
With Transient Memory
Sample
Estimate
Figure 13: h-model's Adaptability From Very Sparse Observations. Posterior Samples at Different Active Target Discovery Phases. Overhead Object Discovery (i.e., Car) with Ground Level images from ImageNet as the Prior. Observation Budget of 300.
32

---

Only Permanent Memory
Target
Sample
Estimate
MART
Transient Memory
TEW
Sample
RUMOY
AV
1/
Estimate
Figure 14: ht-model's Adaptability From Very Sparse Observations. Posterior Samples Different Active Target Discovery Phases. Overhead Object Discovery (i.e., Truck) with Ground Level images from ImageNet as the Prior. Observation Budget of 300.
Only Permanent Memory
Target
Sample
Listimat
With Transient Memory
Sample
Estimate
Figure 15: h--odeels Adaptability From Very Sparse Observations. Posterior Samples at Different
Active Target Discovery Phases. Uncovering Disjoint Balls with MNIST digit images the Prior.
L More Visualizations of the Exploration Behavior of EM-PTDM at Different Active Target Discovery Phases
In this section, we present additional exploration behavior of EM-PTDM at different active target discovery phases. We also provide similar exploration behavior of the baseline approaches, including DifffATD and Greedy Adaptive, for the comparison. These visualizations are provided in Figures [66 17 18 These additional visualizations further reinforce the effectiveness EM-PTDM in addressing active target discovery under uninformative prior.
33

---

Step
Step 3
Step - 60
Step 300
Target
DiffATD
Witt
EM-PTDM
Figure 16: Visualizing the regions explored by each method various stages of the ATD process. In these visualizations, patches corresponding to successful queries are unmasked, while those resulting unsuccessful queries are highlighted in Red. The task focuses on discovering overhead objects (cars), using ground-level images from ImageNet as the prior. The results demonstrate that EM-PTDM effectively identifies and explores most of the target regions containing cars.
Step -
Step - 3
Step 60
Step 300
Target
GA
EM-PTDM
Figure 17: Visualizing the regions explored by each method various stages of the ATD process. In these visualizations, patches corresponding to successful queries are unmasked, while those resulting unsuccessful queries are highlighted in Red. The task focuses on discovering overhead objects (trucks), using ground-level images from ImageNet as the prior. The results demonstrate that EM-PTDM effectively identifies and explores most of the target regions containing trucks.
Step
Step 3
Step 60
Step 250
Target
GA
EM-PTDM
Figure 18: Visualizing the regions explored by each method at various stages of the ATD process. In these visualizations, patches corresponding to successful queries are Green, while those resulting in unsuccessful queries are highlighted in Red. The task focuses on uncovering Disjoint Balls from MNIST digit images as the Prior. EM-PTDM discovers most target regions (i.e., Disjoint Balls).
34

---

M Active Target Discovery of Balls Using MNIST Images as the Prior
To enable comprehensive analysis of EM-PTDM, we introduce a custom-designed dataset tailored for this task. It simulates active discovery scenarios involving an unknown number of balls with unknown locations and radii, with MNIST images as the prior. Success this setting requires effective exploration of the search space to accurately localize the targets, capturing the core challenge of the problem. The details the proposed dataset are provided below.
M.1 Dataset Creation Procedure
In this dataset, we generate each sample by randomly placing 5 to 10 identical balls within 32x32 2D grid. The radius all balls in a given sample is either 4 pixels, randomly selected per sample. All placements are performed uniformly at random, subject to the non-overlapping constraint and the boundary condition that each ball lies entirely within the 32x32 space.
M.2 SR Comparisons with Baseline Approaches
As in previous settings, we quantitatively evaluate EM-PTDM and baseline methods using the Success Rate (SR) metric. In this experiment, the task involves actively discovering target balls using a diffusion model trained on the MNIST dataset as the prior. The results, summarized in Table show consistent trend: EM-PTDM significantly outperforms all baselines across different measurement budgets. This further reinforces the effectiveness of EM-PTDM in handling active target discovery under an uninformative prior.
Table SR Comparison with Baselines.
Active Discovery of balls with MNIST Digit Images as Prior.
Method
B = 150
B = 200
B = 250
RS
0.1458
0.1826
0.2187
DifFATD
0.4362
0.4432
0.4929
GA
0.3250
0.5170
0.6257
EM-PTDM
0.5561
0.6856
0.7875
M.3 Analyzing the Exploration Strategies of EM-PTDM and DifFATD Under Increasing Task Complexity
In this section, we provide additional visualizations highlighting the exploration behavior of EM- PTDM and DifTATD across different stages of the active target discovery task. Using the task of discovering target balls with MNIST images the prior, the visualizations in Figures 19 clearly show that EM-PTDM consistently explores more effectively and identifies targets with hig her accuracy, even under increasing task complexity while adhering to strict budget and under an uninformative prior. These results further underscore the robustness and adaptability of EM-PTDM in challenging discovery scenarios, where efficient exploration of the search space is the key. A striking emergent behavior is observed across both examples: the early stages of the active discovery process, EM-PTDM engages in broader exploration of the search space compared to DiffATD. This initially results in fewer target discoveries (e.g., at step 60). However, this strategic exploration enables EM-PTDM to build richer understanding of the environment, which it later exploits to surpass DiSTATD, ultimately identifying a greater number of target regions before the observation budget is depleted (see step 250).
20
35

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Step
Step
Step 60
Step 250
Target
DifFATD
EM-PTDM
Figure 19: Visualizing the regions explored by each method at various stages of the ATD process. In these visualizations, patches corresponding to successful queries are highlighted in Green, while those resulting in unsuccessful queries are highlighted in Red. The task focuses uncovering Disjoint Balls from MNIST digit images as the Prior. The results demonstrate that EM-PTDM discovers most target regions (i.e., Disjoint Balls).
Step =
Step = 3
Step = 60
Step = 250
Target
DifTATD
EM-PTDM
Figure 20: Visualizing the regions explored by each method at various stages of the ATD process. In these visualizations, patches corresponding to successful queries are highlighted in Green, while those resulting in unsuccessful queries are highlighted in Red. The task focuses on uncovering Disjoint Balls from MNIST digit images the Prior. The results demonstrate that EM-PTDM discovers most target regions (i.e., Disjoint Balls).
N Architecture, Training Details: h- model, Pretrained Diffusion Model, and the Reward Model; and Computing Resources
N.1 Details of h-model
For the MNIST-to-Ban tasks, we employ 32-dimensional diffusion time-step embeddings and single-block U-Net f-model with layer widths of [32, 64]. In the species discovery tasks, also use 32-dimensional time-step embeddings, but with a single-block h-model featuring wider layers [32, 64, 128]. For the ImageNet-to-DOOe tasks, increase the embedding dimensionality to 128, using a similar single-block h-model with widths [32, 64, 128]
N.2 Details of Reward Model
Our proposed method, EM-PTDM, utilizes parameterized reward model, Ty. to steer the exploitation process. To this end, we employ a neural network consisting of series of convolutional and fully connected layers, with non-linear ReLU activations the reward model (r,)). The reward model's
36

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goal is to predict score ranging from O to I, where a higher score indicates a higher likelihood that the measurement location corresponds to the target, based on its semantic features. Note that the size of the input semantic feature map for given measurement location can vary depending on the downstream task. For instance, when working with DOTA, we use an 4 x patch as the input feature size. After each measurement step, we update the model parameters (r) using the binary cross-entropy loss. Additionally, the training dataset is updated with the newly observed data point, refining the model'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 consists of I 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 size)? to an output of size 4 with weights
and biases of size (imput size)? 4] and [4] respectively. The second FC layer transforms an input of dimension 4 to an output of size 32 with 2-dimensional weight of size [4, 32] and a bias of size [32]. The third FC layer maps 32 inputs 16 outputs via weight matrix of shape [32, 16] and a 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 an output of size 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 binary cross-entropy loss. The reward model is trained incrementally for epochs after each measurement step using the gathered supervised dataset resulting from sequential observation, with a learning rate of 0.01.
N.3 Details of Primary Memory as Pretrained Diffusion Model
We use DDIM [2] as the diffusion model across datasets. The diffusion models used in different experiments are based on widely adopted U-Net-style architecture. For the MNIST 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. For DOTA, we use the input feature size of [128, 128, 3). the architecture featuring 128-dimensional time-step embeddings and a diffusion model with 2 residual blocks of width 664, 128, 256, 256, 512]. Finally, all experiments are implemented in Tensorflow and conducted on NVIDIA A100 40G GPUs Our training and inference code will be made public.
Statistical Significance Results of EM-PTDM
In order to strengthen our claim on EM-PTDM's superiority over the baseline methods, we have included the statistical significance results with different active target discovery settings, and present the results in Tables I0 II These results are based on independent trials and further strengthen our empirical findings, reinforcing the stability and effectiveness of EM-PTDM in tackling active target discovery under an uninformative prior across diverse domains.
Table 10: Statistical Significance Results for Unknown Overhead Object Discovery.
Active Discovery of Overhead Objects with Ground Level ImageNet Images the Prior.
Method
B = 250
B 300
B 350
RS
0.2325 0.0190
0.2852
0.0137
0.3207 + 0.0168
DiffATD
0.5143 + 0.0067
0.6391
+ 0.0102
0.7348 +: 0.0041
GA
0.4784 0.0122
0.5659
0.0096
0.6562 + 0.0054
EM-PTDM
0.5620 = 0.0073
0.7013 = 0.0038
0.8256 = 0.0093
37

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Table 11: Statistical Significance Results for Unknown Species Discovery Task.
Active Discovery of Species CS with Species GG as the Prior.
Method
B 150
B 200
B 250
RS
0.1624 + 0.0133
0.2327 0.0201
0.2775 + 0.0154
DifFATD
0.3420 + 0.0115
0.4365 = 0.0057
0.4808 = 0.0063
GA
0,4061 + 0.0047
0.5067 0.0079
0.5567 = 0.0085
EM-PTDM
0.4983 + 0.0060
0.6495 + 0.0T08
0.6989 + 0.0056
P Impact of Weak Permanent Memory on Active Target Discovery Performance
When extremely weak prior is used as the permanent memory, according to Equation (6), adapting to new domain essentially reduces to learning the task from scratch through the transient memory alone. In this case, as indicated by Equation (7), the h-model no longer serves as corrective mechanism; instead, under a partially observable environment, the entire responsibility for modeling the posterior shift falls this lightweight module. However, this is beyond the capacity of such lightweight module by design. In order to validate our hypothesis, we perform additional experiments under a remote sensing scenario. where deliberately replaced the permanent memory with diffusion model that could only output noise without any meaningful semantic structure. On top of this setup, we implemented EM-PTDM and observed the following phenomenon: even h-model was updated under partial observations, its limited capacity made it insufficient to compensate for the lack of meaningful prior. As result, all of the unexplored regions of the posterior estimation remained dominated by the weak prior essentially resembling noise leading to poor global environment estimation. We present our findings in the following Table 12 This supports the claim that an extremely weak or non-semantic prior forces the transient memory to handle an unrealistically large modeling responsibility, which goes beyond its design capability.
Table 12: Analysis of Weak Permanent Memory: Performance Comparison on DOTA
Method
B = 250
B 300
EM-PTDM (Random Noise as Permanent Memory)
0.3117
0.3465
EM-PTDM (ImageNet as Permanent Memory)
0.5620
0.7013
Q More Details on Computational Cost across Search Space
We have conducted a detailed evaluation of sampling time and computational requirements of EM- PTDM across various search space sizes. We present the results in the following table. Our results (as reported in [3] show that EM-PTDM remains efficient even as the search space scales, with sampling time per observation step ranging from 0.83 to 1.87 seconds, which is well within practical limits for most downstream applications. This further reinforces EM-PTDM's scalability and real-world applicability.
Table 13: Details of Computation and Sampling Cost Across Varying Search Space Sizes
Active Discovery of Handwritten Digits
Search Space
Computation Cost
Sampling Time per observation step (Seconds)
28 x 28
0.78 GB
0.83
128 128
1.51 GB
1.87
38

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R
Code Link
Our code and models are publicly available at this link
39


Reviews:
[{"review_id": "nD0ajrPXsa", "reviewer": "Reviewer_XAtE", "summary": "This paper proposes a principled framework EM-PTDM to tackle Active Target Discovery (ATD) in scenarios where no informative prior exists—a situation often faced in domains like rare species detection or novel object discovery. The method consists of two components:\n(1) Permanent Memory: a pretrained diffusion model capturing general knowledge; (2) Transient Memory: a lightweight, adaptive h-transform module that quickly adjusts to task-specific signals. The method uses an EM-style iterative refinement and principled sampling strategies balancing exploration and exploitation. Experimental results on species distribution and remote sensing show notable improvements over baselines, even under severely uninformative priors.", "questions": "See Cons.", "limitations": "N/A", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Pros:\n* The paper clearly identifies a relevant gap: active search without any informative prior, which is highly practical in many scientific fields. \n* Drawing parallels to permanent and transient memory systems in the brain is creative and helps frame the proposed method intuitively. \n* The EM update of the prior and the integration of the h-transform for conditional sampling are well-motivated and mathematically rigorous. \n* The method shows clear empirical gains over baselines, especially in low-data regimes.\n* The paper provides code and uses public datasets, which facilitates reproducibility.\n\nCons:\n* The paper is quite dense and could be hard to follow for readers without a strong ML background. Adding simpler diagrams or pseudocode could help.\n* The authors mention instability if the h-model is updated too often early on. It’d be helpful to see how sensitive the results are to different update frequencies.\n* While the method beats strong baselines, many of those still rely on prior knowledge. It would be good to test simpler baselines too—for example, training on random samples and then re-ranking spots based on how similar they are to places where targets were found, without retraining the diffusion model.", "was_revised": true, "final_justification": "The authors addressed my concerns. However, as I am not deeply familiar with this field, I would prefer to maintain my borderline accept score and defend my assessment.", "rebuttal": "Thank you for your thoughtful and encouraging feedback. We appreciate your recognition of our clear problem framing, the creative analogy to brain memory systems, the rigorous methodological development, the strong empirical results in low-data settings, and our commitment to reproducibility through code and public datasets. Next, we address all your concerns.\n\n> Q1: The paper is quite dense and could be hard to follow for readers without a strong ML background. Adding simpler diagrams or pseudocode could help.\n\n**A1:** Thank you for your helpful suggestion. To address accessibility, we had included several explanations in the Appendix, including simpler diagrams (see **Figure 20 in the Appendix Section W**) and detailed pseudocode (see **Algorithm 1 and 2 in the Appendix Section I**). Following your feedback, we will move some of these explanations back into the main paper to help readers follow the content more easily.\n\n\n> Q2: The authors mention instability if the h-model is updated too often early on. It’d be helpful to see how sensitive the results are to different update frequencies.\n\n**A2:** Thank you for this insightful observation. We agree that updating the $h$-model too frequently during the early discovery phase can lead to instability. To investigate this, we conducted a controlled experiment comparing posterior sample generation when updating the $h$-model after every observation versus after several observation steps. Our results show that frequent updates produce noisier posterior samples, and we provide a detailed discussion of this phenomenon in Section 3 (**see lines 184–208, and Figure 2 for a visualization of this fact**). Building on these findings, we further analyze the sensitivity of the results to different update frequencies in the **Appendix Section R**. Additionally, we propose an adaptive update strategy, described in **Section H.1 of the Appendix**, which dynamically adjusts the update schedule. Empirically, this adaptive approach outperforms fixed-interval update schedules, resulting in improved discovery performance (**See Table 8**). These results highlight the important role that update frequency plays in the stability and effectiveness of the $h$-model, which in turn impact the discovery performance. \n\n> Q3: It would be good to test simpler baselines too—for example, training on random samples and then re-ranking spots based on how similar they are to places where targets were found, without retraining the diffusion model.\n\n**A3:** Thank you for your suggestion. Following your feedback, we compare the performance of EM-PTDM with the suggested approach. We report our findings in the following Table. The experimental outcomes further reinforce the impact of EM-PTDM, and further justify the importance of both Permanent and Transient Memory.  \n\n**ATD Performance Comparison Using DOTA**\n\n|           Method           | $\\mathcal{B}$ = 250 | $\\mathcal{B}$ = 300 | $\\mathcal{B}$ = 350 |\n|----------------------------|------------------|-----------------|--------|\n| Frozen Diffusion with Random Prior |  0.2630 |    0.2979   | 0.3608 |\n| EM-PTDM | **0.5620**  |  **0.7013**   | **0.8256** |"}, {"review_id": "csCYhi0dYf", "reviewer": "Reviewer_MN5m", "summary": "This paper presents a method for diffusion-based active target discovery (ATD), where no prior samples from the target domain are available to learn the diffusion dynamics a priori. Instead, the proposed method uses a combination of a pre-trained diffusion model and a lightweight update mechanism based on Doob's h-transform to modify the prior. Experiments on two problem settings are presented, showing improvements over the main baseline of DiffATD.", "questions": "1. I'm still struggling a bit to understand the terminology of updating the \"prior\". Does this not violate Bayesian principles of encoding beliefs *before* seeing the data? Also, given that we're updating the prior based on very few data points, do you think it is possible that this approach risks overfitting to the presented observations, something that starting with an uninformed prior may not succumb to?\n2. What is the standard deviation one should expect with the experiments shown for each method? Are the current experiments reporting single runs or repeats?", "limitations": "No. To provide a better understanding of capability, it would have been useful if the authors showed scenarios in which their method does not, in fact, perform very well.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The problem setting is motivated well, and the writing/figures are clear.\n- The results on the two problem settings show a clear improvement over a reasonable choice of baselines.\n- The method is rigorously described.\n\n**Weaknesses:**\n- The paper currently only briefly describes the underlying DiffATD method. It would be helpful if the authors add a brief section describing that method to better ground the reader.\n- It's unclear to me whether the two problem settings shown are representative (not a big weakness; but my confidence would be higher with more evaluation settings shown)", "was_revised": true, "final_justification": "I believe the paper addresses an important problem setting and presents a novel method that shows statistically significant improvements over baselines. The authors have adequately provided an explanation to my question about the prior. They also address a few exposition-related concerns promising the addition of certain writing in the final version (DiffATD explanation and Limitations).", "rebuttal": "Thank you for your positive and encouraging remarks. We appreciate your recognition of the well-motivated problem setting, the clarity of our writing and figures, the rigorous description of our method, and the clear performance improvements demonstrated across diverse problem settings compared to strong baselines. Below, we clarify all your concerns.\n\n> Q1: The paper currently only briefly describes the underlying DiffATD method. It would be helpful if the authors add a brief section describing that method to better ground the reader.\n\n**A1:** Thank you very much for your valuable suggestion. We agree that including a brief section outlining the underlying DiffATD method will greatly help readers gain a clearer and more intuitive understanding of the concepts. Following your feedback, we will add a concise and accessible overview of DiffATD in the revised manuscript to better ground the reader and enhance the overall clarity of the paper.\n\n> Q2: It's unclear to me whether the two problem settings shown are representative (not a big weakness; but my confidence would be higher with more evaluation settings shown)\n\n**A2:** Thank you for this question. The problem settings we chose are grounded in real-world applications where active target discovery is critical, such as remote sensing and species discovery. While these scenarios highlight the strengths of EM-PTDM, we believe EM-PTDM establishes a foundational framework for active target discovery and, given its generality, holds significant promise for broader applicability across diverse domains beyond those discussed in this work, including active drug discovery and novel disease detection. We are enthusiastic about exploring these other domains in our future work.\n\n> Q3: I'm still struggling a bit to understand the terminology of updating the \"prior\". Does this not violate Bayesian principles of encoding beliefs before seeing the data? Do you think it is possible that this approach risks overfitting to the presented observations?\n\n**A3:** Thank you for raising this important question. We distinguish between two types of memory in our approach: the permanent memory, which acts as a true Bayesian prior, and the transient memory, which serves as an adaptive correction mechanism. The permanent memory remains fixed during the active target discovery process and is pre-trained on a dataset from a different domain, thereby encoding general, domain-agnostic knowledge before seeing any new observations from the domain of interest. This ensures adherence to Bayesian principles.\n\nIn contrast, the transient memory is updated periodically with newly observed data to capture task-specific context and align the model dynamically with the current environment. Importantly, this transient memory is re-initialized at the start of each new active target discovery task, preventing carryover of task-specific biases and mitigating the risk of overfitting to limited observations. By separating stable prior knowledge from adaptive task-specific updates, our approach balances principled Bayesian inference with the flexibility required for effective active discovery in dynamic, data-scarce settings. We hope this clarifies how our update strategy respects Bayesian principles while enhancing adaptability and robustness.\n\n> Q4: What is the standard deviation one should expect with the experiments shown for each method? Are the current experiments reporting single runs or repeats?\n\n**A4:** This is a great question. We present the detailed standard deviation values across different settings in **Appendix Section X**, offering transparency regarding the variability of each method’s performance. We would like to emphasize that we report all the results in our paper as averages over 5 independent experimental trials to ensure the reliability of our findings. We hope this additional information helps clarify the robustness of our experiments.\n\n\n> Q5: To provide a better understanding of capability, it would have been useful if the authors showed scenarios in which their method does not, in fact, perform very well.\n\n**A5:** Thank you for this insightful suggestion. In our experiments, we observed that when the permanent memory component is extremely weak and doesn't contain any semantically meaningful information for certain active target discovery tasks, the performance of EM-PTDM can be affected. We will include a detailed discussion of these scenarios in the Limitations section of the revised manuscript, which we believe will offer valuable context and guide future research directions. Thank you again for encouraging this important reflection."}, {"review_id": "yd3v6SWtKv", "reviewer": "Reviewer_ztLM", "summary": "The authors study the problem of active target discovery—identifying regions of interest within a discrete domain $\\mathcal{X}$ from a limited number of labelled observations $(x_i, y_i)_{i=1}^N$, where $y$ is a binary label and $N \\ll \\lvert \\mathcal{X} \\rvert$. This setting is closely related to EM algorithm and Bayesian experimental design, but here the underlying model is a generative model $p(x)$, specifically a diffusion model. The goal is to align the generative model to produce samples predominantly from the target region, by strategically selecting which data points to observe.\nTo achieve this, the authors decompose the generative model into two components: a permanent memory represented by the pretrained model, and a transient memory represented by a Doob's $h$-transformed model. During alignment, only the parameters $\\phi$ of the $h$-transform are updated, enhancing sample efficiency. The objective for updating $\\phi$ is designed to guarantee improvement in the model evidence at each step. Similarly, the acquisition function—parameterised by $\\eta$ and used to guide data selection—is also guaranteed to improve with every update.\nEmpirically, the proposed exploration algorithm demonstrates superior sample efficiency compared to existing diffusion-based approaches, such as DiffATD.", "questions": "1. How stable is the training scheme? I could not find any error bars reported in the results. Given that the EM algorithm is known to be potentially unstable, some quantitative measure of variance would help assess robustness.\n2. What is the role of the reward model? From my understanding, the Gaussian mixture fitted to the posterior represents the (approximated) likelihood of $x$ conditioned on $y$, which could be seen as an approximate reward model for the ATD task. Could you clarify why an explicit reward model is introduced?\n3. What is the difference between this work and Variational Search Distribution [1]? I found this work is quite similar.", "limitations": "I could not find a dedicated limitations section in the paper, which is typically included in the conclusion. While the authors may have discussed some limitations elsewhere in the text, it would be helpful to clearly summarise them in the conclusion for the reader.\n\nOne notable limitation is the lack of a global convergence guarantee, while variational search distribution [1] offers. Since the method relies on the EM algorithm, it inherits well-known issues related to stability, slow convergence, and sensitivity to initialization. These concerns have been highlighted in prior work (e.g., [2]) and should be acknowledged.\n\nReference\n[2] \"Singularity, Misspecification, and the Convergence Rate of EM.\" The Annals of Statistics. https://arxiv.org/abs/1810.00828", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The writing is very clear. The authors do an excellent job of presenting complex algorithms in a digestible and accessible manner.\n- The connection between neuroscience and statistical modelling is novel and insightful. I hadn’t previously considered a statistical decomposition of prior and update terms as analogous to brain functions.\n- Theoretical contributions are well-motivated. Each major component—inference, model decomposition, and acquisition scoring—is supported by a corresponding theorem ensuring step-wise improvement. While overall convergence is not yet guaranteed, these results already represent substantial contributions.\n\nWeaknesses\n- The acquisition component is relatively unclear. I found it difficult to follow the details of the reward model and its necessity in the overall framework.\n- While the EM algorithm is known to be unstable, the authors propose heuristics—such as selectively updating the model rather than after every observation—that help mitigate this issue.\n- Variational Search Distribution [1] has researched a very similar task and methodology, which should be compared and discussed in my opinion.\n\nReference\n[1] ICLR 2025, https://arxiv.org/abs/2409.06142", "was_revised": true, "final_justification": "The authors adequately addressed my concerns. So I remain my acceptance and increased the confidence from 3 to 4.", "rebuttal": "Thank you for your thoughtful and encouraging feedback. We are glad to hear that the clarity of our writing and presentation of complex algorithms resonated well. We appreciate your recognition of the novel and insightful connection between neuroscience and statistical modeling, as well as your positive assessment of our well-motivated theoretical contributions and the rigorous support provided by our theorems. Next, we clarify all your concerns.\n\n\n> Q1: While the EM algorithm is known to be unstable, the authors propose heuristics—such as selectively updating the model rather than after every observation—that help mitigate this issue.\n\n**A1:**  Thank you for highlighting this important point. To address the instability, we introduced selective model update strategy, and provided both qualitative and quantitative evidence demonstrating its effectiveness. We appreciate your attention to this aspect and hope our results clearly illustrate how these strategies mitigate instability in practice.\n\n\n> Q2: How stable is the training scheme? I could not find any error bars reported in the results. Given that the EM algorithm is known to be potentially unstable, some quantitative measure of variance would help assess robustness.\n\n**A2:** \n* Thank you for raising this important question regarding the stability of our training scheme. We provide a detailed analysis of the training dynamics in **Appendix Section M**, where we track the L2 distance between the ground-truth and predicted posterior after each update of the $h$-model (transient memory). Our observations reveal that this distance decreases exponentially as the number of update steps increases, indicating rapid convergence of the $h$-model. We see a similar pattern when comparing the predicted and ground-truth targets, further reinforcing the model’s effective learning.\n\n* To directly address concerns about stability, we followed your helpful suggestion and conducted additional experiments using 5 different random seeds. For each run, we recorded the training loss of the $h$-model—as defined in Equation 7—after every update step. The aggregated results, summarized in the table below, demonstrate that the variance in training loss across these independent trials is minimal. We will add a variance plot of training loss across different observation steps in the updated version of our paper. This consistency strongly suggests that our training procedure is stable and robust, exhibiting reliable convergence behavior regardless of initialization. We appreciate your insightful feedback, which helped us strengthen this aspect of our evaluation and provide a clearer understanding of the robustness of our approach.\n\n**Variance of Training Scheme:**\n\n| Observation Step = 150 | Observation Step = 300 |\n|------------------|-----------------|\n|  0.0197$\\pm$0.0003 |   0.0425$\\pm$0.0011   |\n\n\n\n> Q3: I found it difficult to follow the details of the reward model and its necessity in the overall framework. What is the role of the reward model? Could you clarify why an explicit reward model is introduced?\n\n**A3:** Thank you for your insightful question about the role and necessity of the reward model in our framework. The explicit reward model is crucial to guiding active target discovery within our approach. Our sampling strategy is based on a composite score that balances exploration and exploitation, as defined in Equation 11. The exploitation component (as defined in Equation 10), in particular, represents a reward-weighted expected log-likelihood, where the reward for each unobserved region is estimated using an incrementally trained reward model. This reward model is therefore essential for accurately evaluating and prioritizing candidate regions, enabling our method to efficiently target areas with higher potential for discovery. We provide a concise discussion of these mechanics in **Lines 238–258** of the main text, with further implementation details available in the **Appendix Section V**. For a visual overview, **Figure 20** in the Appendix illustrates how the reward model integrates into the overall EM-PTDM framework and enhances its effectiveness. We appreciate this opportunity to clarify the importance of the reward model, and we hope that these references help shed light on its central role in our proposed approach.\n\n> Q4: What is the difference between this work and Variational Search Distribution [1]? I found this work is quite similar.\n\n**A4:** Thank you for bringing up the Variational Search Distribution (VSD) paper—it's a valuable and relevant comparison. While VSD and our work share some surface similarities in addressing efficient search strategies, there are several fundamental distinctions that set ATD apart: \n* Data Assumptions: VSD operates under the assumption that supervised label data from the target domain is available, including examples from the target class. In contrast, ATD is specifically designed for scenarios where no supervised labels are accessible prior to deployment, making it suitable for real-world settings with severe data scarcity. \n* Domain Priors: The VSD framework leverages explicit domain priors, whereas ATD is tailored for situations where such prior information may be sparse, incomplete, or entirely unavailable. \n* Data Types and Problem Focus: VSD primarily focuses on discrete and semi-discrete design spaces. ATD, on the other hand, is devised to handle continuous, spatially structured, and partially observed environments—such as those found in medical imaging or ecological field discovery—which pose unique challenges not addressed by VSD. \n* Search Setup: VSD conducts search over large-scale, fully accessible databases or pools of candidates. In contrast, ATD targets the discovery of target-rich regions within a single, partially observed instance—requiring strategic querying and reasoning about unobserved areas within a sample. \n\nWe will include the suggested reference in the related work section. \n\n> Q5: I could not find a dedicated limitations section in the paper, which is typically included in the conclusion. While the authors may have discussed some limitations elsewhere in the text, it would be helpful to clearly summarise them in the conclusion for the reader.\n\n**A5:** Thank you for this suggestion. In response to your feedback, we will clearly summarize the limitation and ensure they are explicitly included in the conclusion section of the revised paper.  \n\n> Q6: Since the method relies on the EM algorithm, it inherits well-known issues related to stability, slow convergence, and sensitivity to initialization. These concerns have been highlighted in prior work (e.g., [2]) and should be acknowledged.\n\n**A6:** Thank you for pointing this out. We will certainly acknowledge the prior work as you suggested in the updated version of our paper."}, {"review_id": "V8ao2xU6kz", "reviewer": "Reviewer_VRrR", "summary": "This paper introduces EM-PTDM (Expectation Maximized Permanent Temporary Diffusion Memory), a novel framework for Active Target Discovery (ATD) designed specifically to operate effectively in environments with uninformative or unavailable priors. The core problem addressed is that existing methods, such as DiffATD, perform poorly when domain-specific data for learning a strong prior is scarce.\nInspired by dual-memory systems in the human brain, the proposed method combines a large, pre-trained diffusion model as a \"permanent memory\" for generalizable knowledge with a lightweight, adaptive module based on Doob's h-transform that serves as a \"transient memory\" for rapid, task-specific adaptation. The framework uses an Expectation-Maximization (EM) style algorithm to guarantee monotonic improvement of the prior with new observations. The sampling strategy intelligently balances exploration and exploitation, and the entire approach is demonstrated to significantly outperform baseline methods across challenging domains, including species discovery and cross-view remote sensing.", "questions": "I thank the authors for their work and clear paper. I am open to changing my ratings depending on the discussion of the following points:\n1. What happens when a weak pre-trained diffusion model is used for the permanent memory? I believe this could be addressed by adding some flexibility in altering this part of memory, in a conservative way. \n2. I believe the statement that this is performing under an Uninformative Prior is misleading and not truly precise since the work highly leverages the existence of a pretrained diffusion model. I would appreciate this being addressed. Since this is essentially the main contribution, I think it’s relevant to justify this better. Indeed, this is not task-specific prior domain data, as described in the contributions, but it would be relevant to study how this truly affects the performance. \n3. Equation (10) has text over it.", "limitations": "The authors did not address the limitations of this work, which I believe exist. They are described both under Weaknesses and Questions.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The conceptual framework is highly original. The inspiration from neuroscience's dual-memory systems provides a compelling narrative and a principled design. The technical implementation is equally novel, combining a pretrained diffusion model with a lightweight Doob's h-transform module to separately model permanent and transient memory. This decomposition of the posterior score is an elegant and powerful idea.\n\n- The paper provides theoretical guarantees for the monotonic improvement of the prior with each new observation (Propositions 1 and Theorems 1, 2), which in turn leads to more accurate sampling scores (Theorem 4). This theoretical rigor adds significant weight to the contribution.\n\n- The experiments are thorough and well-designed:\n\ni) Challenging Tasks: The evaluation on both species distribution modeling (uninformative prior from a related domain) and overhead object discovery (cross-view prior from a disjoint domain) convincingly demonstrates the method's robustness and adaptability.\n\nii)  Strong Baselines: The comparison against relevant baselines, including the prior state-of-the-art (DiffATD), clearly shows the superiority of EM-PTDM.\n\niii) Insightful Ablations: The ablation studies effectively validate the core components of the design, such as the importance of the transient memory h-model (Figure 5) and the scheduler for updating it (Figure 2).\n\nWeaknesses:\n- The paper proposes to tackle a critical and practical limitation of current active discovery methods: the reliance on strong, domain-specific priors. By enabling effective ATD in data-scarce scenarios, this work proposes to significantly broaden the applicability of these techniques to a wide range of real-world problems, such as discovering emerging diseases or rare environmental hazards. To the best of my understanding, this is only partially true. While it avoids needing a prior for the specific task (e.g., you don't need data on the rare \"CS\" species to find it), the entire framework critically depends on a very powerful, highly informative general-purpose prior in the form of the pretrained diffusion model (\"permanent memory\"). The experiments confirm this: the permanent memory was trained on MNIST, a distribution of known species, or ImageNet. The success of the method fundamentally hinges on this permanent memory providing a strong starting point. The paper does not explore the true \"uninformative prior\" scenario: what happens if the permanent memory is also weak, biased, or trained on a completely irrelevant domain? The claim of operating \"without any prior domain samples\" could be read as more general than the method supports. \n\n       i)  Furthermore, the paper does not discuss the constraints this imposes. In many real-world, data-scarce domains where this method is most needed, a powerful, relevant pre-trained diffusion model might not exist. For example, in discovering novel protein structures or unique geological formations, what serves as the \"ImageNet equivalent\"? The paper's solution works by shifting the data dependency from the specific task to a general domain, but it doesn't eliminate the dependency. This is a practical limitation that is not addressed or described as a limitation of the work.\n\n       ii) Is the rigid separation between the memory systems always optimal? Especially if the task provides many observations that strongly contradict the initial prior. The paper's design is efficient, but it assumes the permanent memory is \"correct\" and only needs to be guided. It doesn't consider scenarios where the permanent memory itself might need some correction during the discovery process.\n\n- The paper rightly emphasizes that the transient memory module is lightweight, enabling rapid adaptation. However, the overall framework still relies on forward evaluations of a large, pretrained diffusion model. A more detailed discussion of the total computational cost per sampling step (in terms of time or resources) would be beneficial for understanding its practical deployment feasibility.\n\n- A rather simple approach to the exploration-exploitation phase, which could potentially be improved and more fine-tuned for this specific application.", "was_revised": true, "final_justification": "After the nice interactions with the authors, I am happy with the discussion, and keep the score as 4.", "rebuttal": "Thank you for your insightful feedback. We are excited to see that you found our conceptual framework highly original and based on strong theoretical guarantees. We appreciate your recognition of our inspiration from neuroscience's dual-memory systems. Thank you for your attention to our comprehensive experiments on challenging tasks, alongside robust baselines and ablations. Next, we clarify all your concerns.\n\n> Q1: What happens when a weak pre-trained diffusion model is used for the permanent memory? I believe this could be addressed by adding some flexibility in altering this part of memory, in a conservative way.\n\n**A1:**\n\n**Discussion on Weak prior (Permanent Memory):** \n\nThank you for your insightful questions. \n\n* When an extremely weak prior is used as the permanent memory, according to Equation (6), adapting to a new domain essentially reduces to learning the task from scratch through the transient memory alone. In this case, as indicated by Equation (7), the $h$-model no longer serves as a corrective mechanism; instead, under a partially observable environment, the entire responsibility for modeling the posterior shift falls on this lightweight module. However, this is beyond the capacity of such a lightweight module by design.\n\n* Furthermore, following your questions, we did few additional experiments under remote sensing scenario, where we deliberately replaced the permanent memory with a diffusion model that could only output noise without any meaningful semantic structure. On top of this setup, we implemented EM-PTDM and observed the following phenomenon: even $h$-model was updated under partial observations, its limited capacity made it insufficient to compensate for the lack of a meaningful prior. As a result, all of the unexplored regions of the posterior estimation remained dominated by the weak prior—essentially resembling noise—leading to poor global environment estimation. This supports the claim that an extremely weak or non-semantic prior forces the transient memory to handle an unrealistically large modeling responsibility, which goes beyond its design capability. We appreciate your insightful question and will include qualitative visualizations alongside the quantitative results presented in the following table to provide a thorough analysis of these aspects in the revised draft. Thank you for your thoughtful feedback.\n\n\n\n**Analysis of Weak Permanent Memory: Performance Comparison on DOTA**\n\n|           Method           | $\\mathcal{B}$ = 250 | $\\mathcal{B}$ = 300 |\n|----------------------------|------------------|-----------------|\n| EM-PTDM (**Random Noise** as Permanent Memory)  | 0.3117  |   0.3465   | \nEM-PTDM (**ImageNet** as Permanent Memory)  | **0.5620**  |   **0.7013**   | \n\n\n> Q2: I believe the statement that this is performing under an Uninformative Prior is misleading and not truly precise since the work highly leverages the existence of a pretrained diffusion model. I would appreciate this being addressed. It would be relevant to study how this truly affects the performance.\n\n**A2:**\nWhen we referred to “uninformative prior,” our intention was to highlight the lack of domain-specific prior rather than the absence of any meaningful semantic information. As we stated in the motivation, our design was inspired by how the human brain handles novel tasks, where long-term memory always exists and contributes, but when facing an unfamiliar scenario, it often performs suboptimally and requires the assistance of a short-term memory module to adapt quickly. Similarly, in our framework, the permanent memory (pretrained diffusion model) provides a general prior, while the transient memory ($h$-transform module) rapidly adjusts to task-specific information. However, we fully agree that \"Uninformative\" is a general term, its precise meaning does vary based on the context. Thus, we will be very careful about the terminology usage.\n\nWe have a detailed discussion with supporting experimental results on the effects of using a weak permanent memory in **A1**. We appreciate your insightful question.\n\n> Q3: Equation (10) has text over it.\n\n**A3:** Thank you for pointing this out. We will certainly fix this in our updated draft.\n\n> Q4: The authors did not address the limitations of this work, which I believe exist. They are described both under Weaknesses and Questions.\n\n**A4:** Thank you for this question. We have observed that when the permanent memory component is extremely weak and lacks semantically meaningful information for certain active target discovery tasks, the performance of EM-PTDM may be impacted. We will include a thorough discussion of these scenarios in the Limitation section of the revised manuscript to provide valuable context and help inform future research directions. \n\n> Q5: A more detailed discussion of the total computational cost per sampling step (in terms of time or resources) would be beneficial for understanding its practical deployment feasibility.\n\n**A5:** This is a great question. We completely agree! Following this suggestion, we have conducted a detailed evaluation of sampling time and computational requirements of EM-PTDM across various search space sizes. We present the results in the following table.\n\n|           Search Space           | Computation Cost | Sampling Time Requirement (per observation step) (in Seconds) | \n|----------------------------|------------------|-----------------|\n| 28 $\\times$ 28 |  0.78GB |    0.83   | \n| 128 $\\times$ 128 |  1.51GB  |    1.87  | \n\nOur results show that EM-PTDM remains efficient even as the search space scales, with sampling time per observation step ranging from 0.83 to 1.87 seconds, which is well within practical limits for most downstream applications. This further reinforces EM-PTDM’s scalability and real-world applicability. We will include these additional details in our updated draft. \n\n> Q6: A rather simple approach to the exploration-exploitation phase, which could potentially be improved and more fine-tuned for this specific application.\n\n**A6:** Thank you for this question. Our sole objective here is to provide a general framework for Exploration-Exploitation phase. Nevertheless, we agree that it can be fine-tuned further according to the requirements of downstream  specific application."}]

Author rebuttal:

Meta-review: This paper presents a novel and principled framework, EM-PTDM, for Active Target Discovery without domain-specific priors, combining a pretrained diffusion model as permanent memory with a lightweight transient memory module. The dual-memory design, inspired by neuroscience, is both original and well-motivated, and the method is supported by strong theoretical guarantees and compelling empirical results across challenging tasks, significantly outperforming prior baselines such as DiffATD. While concerns were raised about clarity, and reliance on a strong pretrained model, the authors addressed these constructively through additional experiments, terminology clarification, and discussion of limitations. 

The novelty and rigor of this contribution outweigh its weaknesses. Before publication, the authors are encouraged to further strengthen accessibility and by clearly highlighting the practical limitations regarding dependence on pretrained diffusion models.
Decision: Accept (poster)