DiffBED: Scaling Bayesian Experimental Design to High-Dimensions
Authors: Adhi Saravanan
Rik Knowles
Gavin Kerrigan
Tom Rainforth
Venue: ICLR 2026 Poster (2026)
Keywords: Bayesian Experimental Design
Active Data Acquisition
Diffusion Models
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Abstract: Bayesian experimental design (BED) is a principled framework for intelligent data acquisition. However, current approaches do not scale to problems with high–dimensional designs, impeding its uptake. We show that this limitation arises predominantly from the difficulty in specifying a likelihood model that remains accurate throughout the design space, and that without this, standard design optimisation procedures lead to a reward-hacking-like behaviour that exploits deficiencies in the likelihood, producing implausible or unrealistic designs.
To overcome this, we introduce DiffBED, an approach based on a novel BED objective that explicitly rewards realistic designs. Realism is captured by a diffusion model, which we guide using information-theoretic experimental design criteria to generate highly informative yet realistic designs. This enables BED at an unprecedented scale: while existing applications of BED have been restricted to design spaces with a handful of dimensions, we show that DiffBED can successfully scale to designing high–resolution images.

Published as a conference paper at ICLR 2026
DIFFBED: SCALING BAYESIAN EXPERIMENTAL DESIGN TO
Adhithya Saravanan"
Rik Knowles*
Gavin Kerrigan
Tom Rainforth
Department of Statistics
University of Oxford
(saravanan, knowles, aenowel,,kerriaann kerrigan, rainforthJestate ox. ac uk
ABSTRACT
Bayesian experimental design (BED) is a principled framework for intelligent data acquisition. However, current approaches do not scale to problems with high- nigh-dimensional designs, impeding its uptake. We show that this limitation arises predominantly from the difficulty in specifying likelihood model that remains accurate throughout the design space, and that without this, standard design optimisation procedures lead to howard-hacking-ie behaviour that exploits deficiencies the likelihood, producing implausible or unrealistic designs. To overcome this, introduce DiffBED, approach based on novel BED objective that explicitly rewards realistic designs. Realism captured by a diffusion model, which guide using pooommtionntheorette experimental design criteria to generate highly informative yet realistic designs. This enables BED at unprecedented scale: while existing applications of BED have been restricted to design spaces with handful of dimensions. we show that DifFBED can successfully scale to designing high-resolution images.
INTRODUCTION
Experimentation, the process by which we gather information about phenomenon of interest, is a central task throughout science and industry. In scenarios where data collection is costly or time- consuming, such drug discovery (Paul et al., 2010; DiMasi et al., 2016) clinical trials (Fogel, 2018), it is natural to seek designs that yield data that maximally informative. This intuition is captured by the framework of Bayesian experimental design (BED) (Lindley, 1956; Chaloner & Verdinelli, 1995; Rainforth et al., 2024; Huan et al., 2024). In BED, we specify probabilistic model of the data gathering process, use this derive formal notion of the expected information gain (EIG) of an experiment for a target quantity of interest, then optimise this EIG to yield designs we expect to maximally reduce our uncertainty. Thanks the coherence of Bayesian reasoning, this framework is naturally suited to adaptively gathering information across several experimental steps, utilising information from previous experiments each sequential decision we make.
Although, in principle, BED can be applied to wide array of tasks, successful applications have historically been limited to simple problems in which the design variables are dow-dimensional (Papadimitriou, 2004; Loredo, 2004; Vanlier et al., 2012; Shababo et al., 2013; Myung al., 2013; Vincent & Rainforth, 2017; Watson, 2017; Dushenko et al., 2020). Developing methods for nigh-dimensional design spaces is thus critical open challenge (Rainforth et al., 2024; Huan et al., 2024), with the problem historically being considered mostly as one of developing scalable EIG estimators (Foster et al., 2019; Goda et al., 2022; Ao & Li, 2024; Huan et al., 2024; lollo et al., 2025a).
In this work, we identify an even more fundamental barrier: the difficulty of specifying a likelihood that faithfully reflects the real-world data- sitaaageeeaaingg process across the entire design space. As the dimensionality of the design increases, model misspecification becomes increasingly unavoidable, since the likelihood must remain accurate over an exponentially growing space. While modern machine learning models succeed by learning structure near the data manifold, experimental design explicitly seeks out information that goes beyond what is already known. This inevitably requires the likelihood to extrapolate into regions where our modelling assumptions are most fragile.
"qqul contribution.

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1.7
BED DifiBD Random
BED
0.9
0.5
DIIBED
10
20
30
40
50
Experiment Index
Figure The incremental EIG achieved each experiment iteration (left) and initial design set chosen (right) for the search experiment presented in Section 6.2, where an eyewitness is asked to provide preferences between that, despite having high EIG values, the designs chosen by BED meaningless pixel noise, but those provided by our Dif BED approach are still realistic and helpful images.
of generated images based on their likeness suspect. We see
Truth
BED
Figure 2: Posterior samples after 50 search iterations for standard BED (left) and Di fFED (right).
The consequence of this previously undocumented issue, illustrated Figure 1, is that directly optimising the EIG causes imperfections in the likelihood to be exploited, resulting in meaningless designs. This failure mode is analogous to reward hacking in reinforcement learning (Manheim & Garrabrant, 2019; Skalse et al., 2022). Namely, although existing stochastic gradient methods fully capable of optimising the EIG even in very nigh-dimensional settings, the resulting designs are unrealistic and lie in regions where the likelihood spuriously overconfident, with the corresponding experimental outcomes being, in reality. uninformative. When BED is applied sequentially to adaptively select designs, this issue further amplified. As shown Figure 2, the resulting designs induce pathological feedback loop in posterior updates, where rather than remaining uncertain, the posterior collapses around an incorrect value.
To overcome these challenges, we introduce Di ERED, novel method for BED in high-dimensional design spaces. While the assumed likelihood is typically misaligned globally, we argue that the manifold of realistic and feasible designs. As
likelihood is often sufficiently well-specified such, Di ffEED revisits the fundamentals of BED by proposing a new utility function that explicitly rewards designs which both highly informative and realistic, and hence, lie in regions of low misalignment. In many practical settings, we have prior knowledge about which designs are feasible, for example through access unlabelled data foundational generative model over the design space, which allows this realism criterion to be specified independently of the experimental outcomes.
DiffBEn uses a diffusion model for its design prior. Designs are then generated by process call information-gue guidde diffusion, where designs are chosen by simulating the reverse-time SDE of this diffusion process, with guidance provided by an estimator for the score of the EIG. This estimator is itself based on combination of Tweedie's 's formula (Robbins, 1956) and existing EIG gradient estimators (Rainforth et al., 2018: Foster al., 2020). Adaptive design then simply updates the EIG estimator to incorporate new observations and reruns the diffusion with this new guidance.
As shown in Figure 1, FEBED produces designs that are meaningful and informative, which in turn enables effective learning about the target quantity of interest (see Figure 2). DiffRED therefore represents the first successful application of BED in high-dimensional design spaces: we show successful deployment of Di ffBED design spaces in excess of 750 000 dimensions, whereas previous BED approaches have rarely been successfully used beyond ~ 20 dimensions. More broadly, this work shows that coupling BED with powerful generative models provides practical pathway for scaling principled experimental design to realistic, high- nigh-dimensional problems, substantially expanding the scope and applicability of BED.
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2 PRELIMINARIES
We begin by reviewing the key concepts underpinning the BED framework. We express our initial beliefs about the target variable of interest, 8, through prior distribution p(0). We also specify a likeli- hood ply {. which gives the probability of possible experimental outcomes given A and a design S. If an outcome y were observed by running an experiment with design &. the information gain (IG) of such an experiment is the reduction in entropy obtained when updating from the prior p(0) to the pos- terior p(0 y. E) (Lindley, 1956), defined as, [y E) = H[p(0)] -p I y. E)] where H [-] denotes the Shannon entropy. Since the outcome is unknown before running the experiment, we instead max- imise the expected information gain (EIG) (Lindley, 1972; Bernardo, 1979; Sebastiani & Wynn, 2000):
EEG((E) = (e [G. E)] = (p(()) p(v10.s) [logp(O y, E) - log p()),
(1)
= Ex p(vl0.E) [log 0, <) - logp(y {)],
(2)
where the last equality follows from Bayes' rule. The EIG is then maximized to produce an optimal design E* = argmaxçcs EIG(E), where E is the space of admissible designs.
Adaptive Design In many applications we are interested in producing a sequence of designs gl == (5'.52....,,"
(5" ,..,,,, (h) yielding data y := (y', " ..?....,''" x*). While the sequence ęliK could be deter- mined statically before observing any data, more performant approach is to select the design ç adap- tively depending on the history D = {(5' . !=? of designs and outcomes prior to step k. In this adaptive setting, the design for the k-th experiment typically obtained by greedily maximising the incremental EIG( DD = Ep(o p(o*)00.""" [log p(y" ( log p(y | This ex- pression is equivalent to the EIG except that the prior, p(0), is replaced with the posterior, p(0)D*=1), which reflects the current beliefs given the history (Chernoff, 1958; Chaloner & Verdinelli, 1995).
Estimating the EIG While the EIG is conceptually appealing, estimating it can be challenging due to the doubly intractable nature of the objective, with a wide variety of approaches proposed to address this, see (Rainforth et al., 2024, Section 3) for a review. However, when the outcome space y is discrete, the outer expectation with respect to the likelihood can be enumerated over. In this case, the EIG is now
yielding a non-nested estimator (Rainforth, 2017; Gal al., 2017)
EIG(E)--- Eyey ply (8) log I ( + 1/ Σ N E ply On, (n log On,
-
(3)
where On ~ p(0) (or On ~ p(0) D()-1)) in adaptive settings) and p(v ( = 1/2 En ply On. S). In practice, we not only want to estimate the EIG, but optimize it. Various stochastic gradient-based methods have been adapted for allowing such EIG maximisation to be done in an effective and scalable manner (Huan& & Marzouk, 2014; Foster et al., 2020; Goda et al., 2022).
Diffusion Models are a powerful class of generative models (Sohl-Dickstein et al., 2015; Lai et al., 2025) that our approach will build on when producing designs. Diffusson models define a forward stochastic differential equation (SDE) which gradually corrupts data with noise and learn reverse process which undoes this corruption (Ho et al., 2020; Song et al., 2021). 1). The forward SDE is
dr:- = f(x,, t) dt + g(t) aw,
To Ho~ po t E ().
(4)
where (20) is a data distribution, f(r,, t) is a drift vector field, g(t) is a noise schedule, and dW, is an increment of a standard Wiener process. The functions f,g are chosen so that pr ) is approxi- mately (0, I). A generative model is obtained by solving the time-reversal of Equation (4), given by
dx; = [f(x,, t) (()) log (x+)) dt + gt) aW..
(5)
where 27 (TT) and dWW, is time-reversed Brownian increment. The intractable score V log Pr (x+) is approximated by neural network (x 1) with parameters ø trained via denoising score matching (Hyvärinen & Dayan, 2005; Song et al., 2021). Sampling xy from a Gaussian and integrating Equation (5) backwards in time yields samples approximately drawn from (o())).
3 DIRECTLY OPTIMISING EIG SEEKS OUT MODEL MISSPECIFICATION
Bayesian experimental design is inherently model-based, with the EIG relying on the assumed likelihood model p(y 0, E) and subjective prior p(0). As such, how well the EIG reflects the true
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expected utility of gathering new data will depend on the accuracy of this model, in particular how well the assumed likelihood approximates the true conditional data- gentratinn process Ptrue 9, g). While the prior provides some protection against needing the likelihood to be accurate across all 6, optimising over & requires the likelihood to remain accurate across the entire design space.
When the designs & are high-dimensional, faithfully modelling y 0, E becomes especially challenging and it is usually not realistic to construct a likelihood that is accurate across all (0, <) pairs. Indeed, the assumed likelihood p(y|0, E) in high-dimensional problems will often itself be a learned function derived from a pre-trained machine learning model. For example, in Figure I our likelihood utilises a fixed encoder that captures semantic content. In such cases the likelihood will only reflect the true Sata-generating mechanism in data regions near where the feature extracting component was trained.
We now show that direct optimisation of the EIG is inherently prone to secking out areas of the design space where the model is misspecified, specifically, it is drawn to regions where the likelihood overconfident. To do this we consider the difference in using the EIG with our model's s likelihood compared with "true" EIG that uses the unknown true underlying data distribution,
TEIG(E) := (0ppp)))ppp (v/e,E) [log Perue (y (, log Pirue [E),
(6)
Bp()) Perreeyy (y 0, <)]] + HiPerue (y ( [)],
(7)
where Perue {) = Pe) Purru 6 {) Equation (7) and the analogous term for FIG(E) yields EIG(E) TEIG(E) + Ep(o) [H(prrue (y () - Hip(y I e, +H[p(y [)] - H[perue (v/ [)]. (8)
MM((S)
This decomposition provides helpful insight into how the EIG behaves when used with an approximate model likelihood. Namely, we can view M(() as a measure on the average degree of model overconfidence across possible 8: it is zero if the likelihood matches the true data generating process and it grows as the likelihood becomes more certain than it should be. Critically, MM() varies across designs, and its presence in the decomposition encourages designs found by directly optimizing the EIG to lie where the likelihood is overconfident.
Moreover, the remaining Hpp(y E)] Hp {)] term typically provides little protection against this desire to move to regions of overconfident likelihoods. In particular, these marginal data distributions will inherently be more diffuse than the corresponding likelihoods, with the averaging over 0 providing regularisation on their predictions. Thus, in high-dimensional spaces it will usually be easy to find designs where we are overconfident in y 0 E. but our uncertainty over O ensures that H[p(y {)] remains high. Thus, even when the likelihood is heavily misspecified, p(y {) and Perue (y ()) will often still be similar for most S. For example, if we have a design very far away from previous designs then misspecified (but still sensible) model will generally produce high marginal predictive uncertainty, even though might be very confident about y when @ is known. As such, the signal from this remaining term will generally not sufficiently counteract M({) and we can expect direct EIG optimisation to seek out designs where the likelihood is overconfident. The effect of this is clearly visible in Figure where direct optimisation of the EIG has led to designs for which the likelihood is very confident about the outcomes given 0, but that actually correspond to meaningless images where a human responder will not be able to provide any reliable preferences.
4 BAYESIAN EXPERIMENTAL DESIGN VIA INFORMATION-GUIDED DIFFUSION
4.1 MISALIGNMENT-AWANN DESIGN SELECTION
Simply improving the fidelity of ply (, not a viable solution in general for overcoming such issues with misalignment: in high-dimensional design spaces, it is not usually realistic to specify a likelihood that is accurate everywhere, and optimisation can amplify even small residual errors. Instead, we accept that misalignment is unavoidable and modify the design objective itself.
Our key observation is that misalignment is not uniform across designs E: there will usually be regions where the likelihood is more reliable and less reliable. e.g. the likelihood will be more reliable for designs close to any data manifold used in its construction. As this reliability is latent, we introduce surrogate penalty r()) that penalises designs for lying outside the regions where we expect good alignment. We then balance informativeness with the surrogate penalty by maximising
U(E)= = a FIG(E) r())
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where 0 is hyper-parameter introduced to trade off informativeness against adherence low misalignment regions. In complex settings, for example where designs are sets of images, a sensible closed form surrogate penalty cannot usually be directly defined. However, in such settings, we often have access to a large set of realistic and feasible designs through unlabelled auxiliary data, such as corpus of natural images, which especially those parametrised by learned functions, we expect the misalignment to be lowest when evaluated realistic designs. As such, natural approach is to model r(E) using a generative model Pret (E) trained on this data to capture distribution over designs. In some cases, we might even be able to use a pre- trained foundation model for Pret(E), rather than learning such model ourselves.
use to learn surrogate penalty. For most likelihoods,
As we expect higher misalignment for designs that have low probability under the reference distribu- tion over designs Pret (f), we set r({) log (C) yielding the D f FBED objective
UlierBeD (E) = a EIG(E) + log (E)
(10)
We demonstrate later that such reference distribution can often be learned from the same data used for learning the likelihood. There are, however, limitations to directly optimising UDa (E), as standard in BED procedures where ({) = EIG((). Firstly, has been shown that the points that deep generative models assign the highest density to are often not themselves reasonable samples (Nalismick et al., 2018). Secondly, state-of-the- models) are often implicit, and do not provide direct or reliable access to (E) Thus, rather than directly optimising Uni thir=a (E), we instead sample from
generative models (e.g. diffusion and flow
p² (E) x exp(Us) sraen (E)) = Pte((E) exp(a. BIG(E)),
(11)
which assigns greater mass near regions of high Fni (E). Sampling { ~~ p(( now ensures that designs are drawn from high-probability regions of (r) while up-weighting those with large EIG, Notably, this approach is compatible with implicit generative design priors, requires no likelihood- dependent training of Pret nor any modifications to the likelihood, and such, is compatible with state-of-the-ars pre-trained generative models.
An alternative perspective Equation (11) is that (5() is the unique solution to the following optimisation problem over distributions q(E) E P(E):
p" (E)
arg max ((E)
E,(e) [E] (LP((E)) a
(12)
where a is the same hyper- parameter that trades off achieving high EIG values with adherence the reference distribution, as measured by the KL divergence. This solution is often referred to as the exponentially tilted distribution (Rawlik et al., 2012).
4.2 DIFFBED: DIFFUSION MODELS AS REFERENCE DISTRIBUTIONS
Having established pE( as our target distribution for producing designs, we now introduce DiffBED, our proposed framework which realises this idea using a diffusion model as the reference generative model Pref in Equation (II). Diffusion models offer state-of-the-an generative quality across images, video, and scientific data. Moreover, their score- based nature naturally enables powerful training-free free guidance methods for sampling from tilted distributions (Bansal et al., 2023; Uehara et al., 2025; Ye et al., 2024; Aamingo-Enniche et al., 2025; Denker et al., 2024), making them uniquely suited to our framework by allowing sampling from Equation (11) without retraining.
Information- Guudded Diffusion We aim to sample from the EIG-tilted distribution p" (E), which can be cast as a stochastic optimal control problem (Uchara et al., 2024; Domingo- Enrich et al., 2025). Intuitively, this works by augmenting the SDE in Equation (5) with an additional term u(E,, t) dt that seeks to push noisy designs & towards regions of high EIG during the generative diffusion process.
Specifically, let (Ee, t) denote a score function associated with (E) that is sfer(Er, t) = Ve. log (E.). where 25 (Eo) (Eo)(Eo) and each (E,) is subsequently defined by the noising process in Equation (4). This score function could be taken from some pretrained diffusion model on samples of Ç, or it can be defined by explicitly defining (ro along with reference drift vector field (x,, t) and noise schedule g(t) that produce a Pr(Er) which is approximately (0, 7). We can then, in principle, draw samples E ~ PE) by simulating the SDE
sn (E,, 1)] di g() atv, de. [u(Ee,)) () S(E,, g(
LE [0, e ~N(0, (13)
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where the additional drift term u(Ee, t) is given by
u(E,, t) - V( s. log (foa(( [exp(a EIG(E)))]-
(14)
This drift u(Se, t) can be interpreted as the gradient of a value function that rewards states & which likely to yield high-EIG design Eu starting from the current noisy sample &.- However, it is intractable due to requiring an expectation over (rel(Co)()), and sampling Eo Pror(Cnls,, (&) would require us repeatedly solve the SDE (5) starting from the current state εr, once per sample.
As such, inspired by recent work on training-free guidance (Chung et al., 2023; Ye et al., 2024), we define Eo(Ee) == (..cttole)) and approximate u(S., t) F g(t)² la EIG((u(E.)], which follows from approximating the intractable Pret (.) by delta function located at its mean. While this is a crude approximation to the full distribution, we find that in practice it provides a sufficient guidance signal for obtaining highly informative designs. This approximation is tractable as Tweedie's 's formula (Robbins, 1956; Efron, 2011; 1; Meng et al., 2021) allows us to exactly calculate EU(E)) in terms of the score function Seel without needing to simulate the SDE (5). For instance, when [(,, 8) = {, and g(t) = v (t)) (i.e., DDPM (Ho et al., 2020) or the VP-SDE (Song et al., 2021)), Tweedie's formula may be written as (o(E)) (Er + (1 at) t))/ Vag. where 0y = exp( f/r ((s) ds), enabling an efficient approximation of Equation (14) that only requires a single evaluation of the score function.
Putting this together, we obtain an approximate sampler for p" (5) by solving the SDE
d& = [(CG,.) t) - g(()² (Sret(Ee: 1) + a 5, (fi()))) dt - -((() dw.
t [ (15)
backwards in time from ęT NO, I). In practice this simply adds a scaled EIG-gradient estimate to the score network at each step, namely Equation (3) if y is discrete, or some alternative EIG gradient estimator like PCE or NMC it is not (see e.g. Rainforth al. (2024, Section 3)).
In sequential settings, Di FRED allows for adaptive design simply by replacing the EIG gradient estimator with an estimator for the incremental EIG, i.e. EIG( (Dk Thus it analogous to the traditional sequential BED approach which chooses designs in myopic way, except that our optimization for each design uses our guided diffusion approach described above. In Appendix B, we present the full details needed to implement Di fEED (c.f. Algorithm 1).
Design Sets: Interacting Particle Diffusion applications such as human preference elicitation,
each design may itself be a ser of S elements < ((()) . _(5)} with g(t) E R and & E R
In such settings, we can leverage standard diffusion model defined on individual elements, {(ي) e
RD, and then set our reference distribution to be an independent mixture of these, i.c., Pref ( x
I (1)) While sampling a design set, we maintain a noisy set & = (sl 5t
(8)
and
the reverse process for each element c. for j = I,..., is given by dcL")
[s(e .1) ((1))(( (Tor((E"") .1) aV (GG(G) di + +((( aw!!
(16)
where (G.)) -
is the set of element-wise conditional means and aW! are independent Brownian increments. Here the diffusion prior contributes an independent score update for each element, ensuring realism, while the EIG term V
cfo EIG(E.) introduces cross-element coupling, ensuring informativeness of the entire set as design. This yields an interacting -patticle diffusion that is structurally similar to diversity-orienter particle guidance schemes (Corso al., 2023; Kirchhof et al., 2025), except that coupling arises from the EIG objective rather than repulsive kernel designed to enforce diversity.
Posterior Inference For sequential BED, we require a fast, high- posterior sampler. In our image-scale experiments, a key design choice of D f FRED is to perform inference in a latent space rather than directly in pixel space. This exploits the fact that, in many ostensibly high-dimensional tasks, the information we care about concentrates in a much lower-dimensional representation (e.g.. perceptual features), while nuisance variation (background, illumination, pixel noise) can be ignored. This choice also aligns with the recent shift toward latent world modelling in areas like robotics (Bar et al., 2025; Garrido et al., 2025; Mei et al., 2026). Operating in this space makes Di DiffBED robust and scalable, while remaining compatible with problems where the likelihood is naturally defined on top of encoder. We provide further details of our particle-based inference scheme in Appendix C.

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5 RELATED WORK
Although the framework of BED has long history (Lindley, 1956; Bernardo, 1979; Sebastiani & Wynn, 2000), scaling BED to realistic settings remains an open challenge (Rainforth al., 2024; Huan et al,, 2024). Viewing this challenge as one of computational costs, long list of works (Foster et al., 2019; 2020; Goda et al., 2022; Ao & Li, 2024; lollo et al., 2025a) have looked to provide improved gradient estimators compared to simple nested Monte Carlo (Rainforth et al., 2018). Notably, Iollo et al. (2025a) also considers the use of diffusion models, but only in an attempt to improve scaling in the target variable space, 0, by using diffusion model for their prior, p(0). All of the aforementioned works are restricted to dow-dimensional design spaces, with the 15-dimensional and 20-dimensional design spaces considered by Iollo et al. (2025b) and Ivanova et al. (2021) respectively being some of the highest dimensional applications of sequential BED. By contrast, we successfully conduct sequential design optimisation in design spaces of over 750 000 dimensions.
Model misspecification has also been studied in the context of BED (Feng, 2015; Overstall & McGree, 2022; Go & Isaac, 2022: Forster al., 2025), with prior works typically looking to address misspecification by explicitly adjusting the model or the EIG itself. We are the first, however, to demonstrate the occurrence of reward hacking- style behaviour and highlight that this is typically unavoidable in high- nigh-dimensional design spaces, especially if the likelihood has been learned from data. Sürer et al. (2024); Oliveira et al. (2024) use a Gaussian Process to correct errors in the model, but are focused on the setting of simulator calibration and assume that dataset of real experimental outcomes already available prior to doing experimental design. In our high-dimensional, low-data setting, learning an explicit bias is not feasible, as it would require large quantities of experimental outcome data, which is fundamentally scarce. Thus, Di E EEEED provides the first scalable solution by instead introducing design prior to regularise the design optimisation.
Recent BED work has also considered leveraging LLMs to generate natural language questions, e.g. for preference elicitation (Choudhury et al., 2025; Kobalczyk et al., 2025); this represents problem where the designs are much higher dimensional and more complex than most traditional appli- cations of BED. In general, these approaches work by generating batch of candidate designs from the LLM, estimating the EIG for each, and then choosing the design with the largest estimate, analogously to the Rank variant of Di f fBED we consider in our experiments. Handa et al. (2024) similarly consid- ers preference elicitation using BED and LLMs, but assumes the parameter and design are supported on an explicit and fixed oow-dimesiional feature space. Unlike these works, D f FBED explicitly focused on high-dinn nigh-dimensional and continuous design spaces, leveraging mudient-based optimization.
EXPERIMENTS
We now perform an extensive empirical evaluation of our proposed Di DiffBDD method. Although DiffBED is not specific to any experimental setting, our experiments are unified by the theme of human feedback elicitation, as this encapsulates a broad range of important, real-world tasks with high- dimensional designs. In particular,
focus the setting where designs consist of one or more im- ages. We consider a range of datasets and feedback types, which include rankings and discrete ratings. We defer in-depth experimental details, including additional results and ablations, the Appendix.
Our primary baseline is the current standard paradigm for BED, namely, direct gradient- based maximisation of an EIG estimator (Huan et al., 2024; Rainforth et al., 2024). We also compare against Entropy, a variant of Di f fBED where we guide the diffusion model with the marginal predic- tive entropy rather than the EIG. We further consider two ranking baselines. Rank (Pool) estimates the EIG for 1000 candidate designs per iteration (chosen to roughly match the runtime of Di E BEDD) and selects the highest EIG candidate. To make this baseline as strong as possible, candidates are drawn directly from the data used to train the diffusion model, rather than being generated. Rank (Diffuse) instead samples candidates from PE) via the diffusion model, as required when no pool is available. Under compute normalisation this corresponds to N x 4 candidates (Appendix B.3); we use N 5 to conservatively allocate more compute to Rank (Diffuse). Finally, we compare against Random, simple baseline where designs selected uniformly at random from set of feasible designs.
Baselines
To evaluate the different design strategies, we track our ability to recover a ground truth target variable feree- For the drcation-findigg task, we report the mean L2 error between the ground truth 0rne and samples from the current posterior over f. For our image-space experiments, we instead report the mean cosine similarity between Orne and samples from the current posterior. We
Metrics
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DiMBED
L.2 Error
Entropy
BIG
10-1
Rank (Pool)
Rank (Diiffuse
3.
Random
BED
20 Experiment Index
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30
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Figure 3: Incremental EIG (under Pmodel) at each experiment iteration (left) and average L2 error be- tween posterior samples and ground truth locations (right) for the source location finding experiment. DiffBED achieves the lowest L2 error, with traditional BED and the rank methods all doing poorly.
also evaluate the incremental EIG of the chosen design at each step, but emphasise that this should not be viewed as a success metric itself but rather an insightful quantity to track. We additionally include several qualitative results (c.f. Figures and 2). Results source location finding and MNIST are averaged over 25 random seeds, while CelebA and Zappos are averaged over 10.
6.1 SOURCE LOCATION FINDING
Our first experiment is source location finding, a synthetic problem widely studied in BED (Ivanova et al., 2021; Blau et al., 2022; Iollo et al., 2025a). The goal is to infer the location of N sources 0 = (0(1), ((2) ..... (( E NNxD, each of which emits signal that decays according to an inverse square law, At each experiment, sensor placed at location the signal intensity at ç. The (noiseless) signal strength given by p(0, E) = b + m+1000-si where Ci, b, and m are known constants. The observed signal follows a log- nornnramll distribution log y E ~ NNog (f, r.. We use Pmodel 0, {) to represent this assumed likelihood.
I records noisy measurement y E E of
As this problem does not use a learned likelihood, we explicitly introduce model misalignment to illustrate the utility of Di Diff We assume that there is region of design space E* C which is well-aligned, i.e., where Pmodel captures the data generating process. Outside of this region, we assume that data is drawn according to an out-of distrrtiibttion likelihood Pood 0, E). leading to the mixture Perue (y)0, 1s- (m))))eee(y
+ (1 1 (E)) (y)0, g). We take 3 to be collection of cight disjoint circles. For Pood we use the same form as Pmodels except with different choices for a, leading to systematically lower signal mean when & E" Inference is done using Pmodel The reference Pref(S) (5) is taken to be mixture of Gaussians, centred on E". See Appendix D.
As seen in Figure 3. BED produces designs with high incremental EIG estimates, but it often produces designs outside of E This leads to out-of-distribution data, hampering inference and resulting in T.2 error which is worse than random draw from peet (E). Interestingly, Rank (Pool) considers far more candidates than Rank (Diffuse) (1000 vs. 5). yet achieves worse L2 error. This is because Rank greedily selects the highest EIG candidate under Pmodel, and larger set of candidates is more likely to contain designs that are unlikely under Pref, again yielding This mirrors a phenomenon in active learning, where the performance of BALD can degrade as the candidate pool grows, partly because larger pools contain more unlikely inputs (Bickford Smith et al., 2023). Further, as designs are greedily chosen based on a noisy estimate of the true EIG, larger pools exacerbate "winner's curse" effects: the top-ranked design is increasingly likely to be chosen due to estimator noise rather than genuine informativeness. The cumulative effect of these pathologies is seen also in the EIG, where the incremental EIG increases interestingly starts to increase again as the posterior becomes degenerate at later experiment iterations.
data.
These pathologies are mitigated by Di ffBED. Although Di fBED attains lower incremental EIG under Proodel during optimisation, directly generates designs in E" rather than selecting from an increasingly large candidate pool, effectively guarding against misalignment. This translates into substantially better learning, with DiffBED recovering the true source locations to high precision.
6.2 APOOMATION-TIIEOREE SEARCHI
We now evaluate DiffBED high- dishniinessionl,, information-thhorrcee search tasks, where the goal to recover ground-trus -ruth image based on user feedback. Here, designs are sets of images and the outcomes y are rankings indicating the relative similarity of each design to ground-truth image.
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Ground Truth g(
8:20
Ground Truth
g
<(3)
(())
g!4)
((
g
Figure 4: Design sets of four images generated by DiffBEL for CelebA Search, against two ground truths (top and bottom row), experiment iteration 1 (centre, both rows) and 40 (right, both rows).
15
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Figure 5: EIG and cosine similarities for search (mean with + std. error shading), where designs are sets of four images and responses are the rank of the top-two candidates. Di Diff achieves the high- est mean cosine similarity, while standard BED fails to solve the task despite achieving high EIGs.
As motivating example, suppose an eyewitness of a crime being interviewed in order to construct possible images of the suspect that wish to be perceptually close to the true suspect. Though it is not generally possible for the eyewitness to directly generate accurate images, they likely can positively identify photo of the true suspect if shown one and more generally provide feedback when shown images. We can therefore instead iteratively show the eyewitness sets candidate images E = (g(2), ..'"),... ,,,)).())))) (())) and have them provide feedback by ranking the images by how well they match the suspect. Such approach has historically been deployed by UK police forces, but with software that uses low-resolution images and chooses them in heuristic manner (VisionMetric, 2019).
To apply BED, require model approximating the complex relationship between the design & and the ranking Since a person's 's perception of images does not operate at a pixel-by-pixx resol resolution, we assume model (y () where 0 is rich, sufficiently high-dimensional feature space coding of image and our likelihood based around the similarity of each { to underlying Otrue- For our experiment setup, a simulated participant is given a set of S = 4 images and their response, y, is ranking of the top M images. We evaluate D f fBED on MNIST and CelebA (LeCun et al., 1998; Liu et al., 2015), where 0 is obtained using SimCLR embeddings (Susmelj et al., 2020; Chen al., 2020) for the former and a pre-trained VGGFace2 model (Cao et al., 2018) fine-tuned using triplet loss for the latter. Although we do inference in an embedding space, these embeddings can decoded to yield posterior samples image space. See Appendix A and Appendix
We plot the EIG and cosine similarities between posterior samples and Otrue in Figure 5. While standard BED obtains high EIG under Pmodel, model misalignment leads to designs that are indistinguishable from pure noise (Figure 1). Thus, the given preferences are meaningless, yielding a near zero cosine similarity throughout. In contrast, Di DiffBED produces realistic designs (Figure 4) with high EIG. Although DiffBED obtains lower EIG than standard BED, method deliberately trades off EIG for realism. This enables DiffBED to effectively determine 0trecs achieving the high- cosine similarity. Notably, Di f FEBED outperforms Rank (Pool) despite only generating single

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Figure 6: Example high resolution designs produced by Di LffBD on the Zappos dataset.
Cosine Similarity
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Figure 7: Search on the large-scale Zappos dataset with high-resolution (512 x 512) images. Designs are single images with discrete ratings as responses. Even at this scale, DiffRED remains effective.
design set at each iteration, whereas Rank (Pool) considers 000 candidate design sets. Qualitatively, DiffBED first explores diverse, coarse attributes (e.g., gender, hair colour), before refining to more nuanced details in later iterations (Figure 4). This is in contrast to predictive entropy (Entropy) which does in any way encourage the set of images the user is asked to rank to be different, with the EIG needed to capture the nuance that the rankings need to be informative, not simply uncertain.
6.3 TEXT-TO-IMAGE FOUNDATION MODELS
We now scale DiffBED even further by leveraging text-to-image foundation models as pref, focusing on the problem preference elicitation for e-commerce products. Specifically, we consider a setup where the user is shown a single image of shoe and asked to give rating of 1 to 5, using this to hone on the users notion of an "ideal shoe" that we can use for making recommendations. For Pref and Sref, we use Stable Diffusion v1.5 (Rombach et al., 2022), 1B parameter foundation model, fine-tuned on the Zappos (Yu & Grauman, 2014) dataset of high resolution (512 512) modelled by the Ordinal Logit Model which assumes the discrete
images of shoes. Ratings score is correlated with an underlying reward proportional to the similarity the design image to the image of the user's 's ideal shoe. See Appendix A.3.3.
Figure 7 shows that standard BED again fails to learn anything meaningful, while DiffBED produces highly informative designs that also highly realistic (Figure 6). Overall, DiffBED outperforms baselines except Rank (Pool), and even there the gap is only marginal. The performance gap between DiffBED and Rank variants will generally widen when the of sub-designs that need to be chosen (c.g. sets of images to be compared) grows, noting the relatively weaker performance of Rank seen in 6.2 where designs are sets. In such cases, Di f BEED leverages gradient information to directly generate informative design sets, whereas Rank must evaluate many random combinations (by chance) identify an informative one. As such, we expect DiffBED to transfer naturally to batch design, where multiple experiments are designed at each stage by optimising a joint EIG objective (Rainforth et al., 2024).
CONCLUSION
We have shown that model misalignment is a key barrier in scaling BED to high-dimensi ditt-dmmenionnll design spaces, and that when the likelihood is unreliable, optimising standard intomatiion-hhorettii objectives can induce reward-hie heward-hacking behaviour, producing meaningless designs. To address this, we introduced DiffBED, which explicitly trades off EIG against design realism, captured by a reference design distribution. We actualise this by guiding a diffusion model with information-theoree steering sampling towards designs that are both realistic and highly informative. By mitigating the exploitation of model misalignment, DiffBED enables BED with image-scaa scale designs for the first time. Our results on challenging preference elicitation tasks demonstrate that explicitly incorporating design realism opens the door to applying BED in complex domains previously beyond its reach.
objective,
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ACKNOWLEDGMENTS
AS is supported by the EPSRC CDT in Statistics and Machine Learning (EP/Y034813/)) 13/1). RK is supported by the Martingale Postgraduate Foundation. GK and TR are supported by the UK EPSRC grant EP/Y037200/1.
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APPENDIX CONTENTS
A Likelihood Models
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A.I Likelihood PMFs
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A.2 Parametrisation of Latent Reward Model
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A.3 Details of Latent Reward Models
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DiEFBED Details
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B.1 Reference Models
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B.2 Sampling
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B.3 Number of Function Evaluations (NFEs)
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C Posterior Inference
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D Location Finding
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E Additional Image Experiments
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E.1 CelebA: Active Preference Elicitation
E.2 CelebA: iiformation-Theorele Search
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E,3 Zappos...
25
A LIKELIHOOD MODELS
This section provides details for all likelihood models studied our experiments (Section 6).
When picking an experiment paradigm, practitioners must consider the trade-off between the informa- tion conveyed in given observation (e.g. binary preference, partial ranking), and the cost running said experiment. For example, a full-ranking contains high amounts of information per observation, but may not feasible to collect. We summarize the paradigms studied in our experiments in Table 1.
Table 1: Common paradigms for eliciting human feedback.
Example
Paradigm
Example design
Example feedback
Likelihood
Bradley-Terry (BT) (Bradley &
Binary Ranking (Appendix E)
"Image
Image 2"
Allan, 1952)
Ranking designs
Plackett-Luce (PL) (Plackett, 1975; Luce, 1959)
"Image 1
Image 2
from (Section 6.2)
Image 3"
Ordinal Logit (OL) (Mccullagh, 1980)
Discrete rating (Section 6.3)
"4 out 5 stars"
A.1 LIKELIHOOD PMFS
We now provide the functional form of the likelihood models considered in experiments. Note that all the models leverage latent reward model. ro(E), parametrized by the quantity interest, 0, which assigns score ro(E) E R the design/each element in the design set.
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Binary Preferences: Bradley-Terry (Bradley & Allan, 1952)
Let ç ((()), be design set of two items. The Binary Brarley-Terry model assumes,
exp(ro((()))
p(u < 5 10.5) exp(ro(((1)) + exp(ro(((11)
Partial Rankings: Plackett-Luce (Plackett, 1975) Let (5()) ((2) (e),...((()) be design set of S items. Suppose observe a partial ranking of the form
glor)) gloz) > ....> gloM), with M S
where o = (01, o2..... RM) is an ordered list of distinct indices indicating the ranked items. the Plackett-Luce likelihood of the observed partial ranking
M = II ==1
exp(ro(f(as)))
p p(y= g(0r) > >g(oa) > .... > g(am) 10,5)
Σ exp(ra(E(1) EWEE
where Cj is the set of items available at stage j. with C₁ = and Cj+1 = C2 (5(1))).
Discrete Ratings: Ordinal Logit (Mccullagh, 1980) Let & being single item, unlike the Bradley- Terry and Plackett-Luce models, which operate design sets. Under the Ordinal Logit model, observations are one of K ordered, discrete categories, modelled under the following PMF:
plu = le ()0)
by (
k = 1= 1,..., K,
with (1) = -1
A.2 PARAMETRISATION OF LATENT REWARD MODEL
As reiterated in the main body of the paper, in the high-dimensional, challenging settings considered in the paper, defining likelihood, p,y10 E), that mimics human behaviour for all {0,5] is extremely challenging. Further, we note that ply {) can often not be directly trained in supervised manner, and practitioners must leverage domain-specific insight. This is especially true in cases in which the 0 of interest is inherently latent, c.g. user preferences. As such, we must often assume the structure of the canonical models. However, all of the models considered above, we must still define latent reward model, (E).
In many problems, e.g. preference-elicitatin the interpretable features that are most pertinent can be identified. In such settings, the following parametrization can be considered: re(E) = 0 d(E) = Ek=1 0gdx (E), of K interpretable features, e.g. alignment to style. In this parametrisation, can be viewed as interpretable preference weights for the K different aspects. In other problems, where such interpretable features can be identified, one can opt for the following parametrisation: ra(E) (E) = cos (0, d(E)) where d(.) is an encoder of & trained in an unsupervised fashion.
A further practical benefit of these parametrisations is that they are data-efficient, arising from the incorporation of task-specific knowledge through the fixed, pre-trained feature extractors, d(-), which should support faster learning. However, we stress that DiffBED is agnostic to the parametrisation of the latent reward model, r-(-), and more generally, the response paradigm and likelihood model used.
Temperature hyper-parameter, 5 In line with common practice, we restrict the range of the latent reward, r({), to a pre-defined range [-1, 1]. for example through normalisation or by computing the reward as cosine similarities, before introducing multiplicative scaling parameter, т, to expand the range to ----,,--]] This enables explicit control over the sharpness of the assumed likelihood model's response distribution. As -1 + 0, the distribution over potential observations for any design across all the models introduced tends to a uniform distribution. On the other hand, increasing - results in peakier likelihoods, and faster shrinkage of the posterior. However, it assigns a stronger belief on the data generating mechanism, if this does not reflect reality, the degree of misalignment with the true data generating process is also increased.
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A.3 DETAILS OF LATENT REWARD MODELS
In this section, we present the specific details of the latent reward models used in our image experi- ments. the search experiments, we leverage unsupervised encoders trained through contrastive losses, to encourage learning general representations of the data. In the preference elicitation experiment, we leverage an interpretable feature extractor.
A.3.1 MNIST SEARCH (SECTION 6.2)
For the MNIST search experiment, we train an encoder using the SimCLR loss (Chen et al., 2020). We leverage simple CNN architecture, with two convolutional layers and fully-connected layer. The embedding dimensionality is K = 32, with projection-head of size P = 512, hyper- parameter for computing SimCLR contrastive losses. The encoder is trained for 50 000 steps, with a batch size of 1 (224. The underlying reward function used in our Bradley-Terry model is (e(() 7 cosine sim(simclr(E). 0), where simelr is our encoder. We take 7 be 10 in Figure 5.
To explicitly incorporate model misspecification into the responses, we leverage a pre-trained dis- criminator that detects out-of- diddsriibution (OOD) MNIST images. For in in-distribution images, the simulated observation y from re-normalised PMF of the rankings that don't 't include any OOD images, and in cases where all images are classed as OOD, the ranking observations are generated uniformly at random.
A.3.2 CELEBA
Search (Section 6.2) We train a CelebA encoder on the CelebA train set. We take a pre-trained VGGFace2 model as our backbone (Cao et al., 2018), and fine-tune it. We remove the original last layer and replace it with a 64 dimensional linear last layer, hence is, 64 dimensional. We freeze the backbone, training only the last layer weights, before unfreezing the final block before the last layer, and fine tuning these weights alongside the last layer's weights. We train using triplet loss, since CelebA includes identity labels. The underlying reward function used our Placket-L.uce model ro (E) = - cosine_simee saieeessmmmmi sim(vvg(E) (E)(E), O), where vgg is our fine-tuned encoder. We take r to be 10. We run the experiment for 50 iterations.
Preference Elicitation (Appendix E) We train supervised feature extractor on the CelebA dataset by fitting a multi-label attribute classifier to predict the following 23 characteristics that have binary labels in the dataset:
Bald, Hair, Straight.Haiz Receding.Fairlines Bangs, Sideburns, Black.Hair, Gray-Hair, Blond_Hair, Brown_Hair, No_Beard, 5.0.Clock.Shadow, Mustache, Goatee, Big.Lips, Nose,ose, Eyeglasses, Smiling, Heavy.Makeupe Wearing Wearing.Necklaco, Wcaring.Earrings:
We leverage a ResNet50 model initialised with ImageNet weights, with the final layer removed and replaced with linear layer that maps to C' = 23. The model is trained for 25 epochs, with a batch size of 128. We use binary cross-entropy with logits, assigning per-attribute positive weights equal to the negative-to-posine posoiivivee sample ratio to correct for class imbalance, and Adam as the optimizer.
We use Bradley-Terry model, with underlying reward being ro({) = - E.' (E) 0,, where d(E) E [ is vector with element de(E) being the ResNet50 classifier probability that attribute i is present in design image.
A.3.3 ZAPPOS SEARCH (SECTION 6.3)
We train Zappos encoder using the SimCLR loss, with K = 64 and P = 512. We leverage ResNet50-based model and initialized with torchvision's retrained ImageNet- (Deng et al., 2009) weights', with the final fully connected (FC) layer removed and replaced by linear projection to a K embedding space. The model is trained 50,000 steps, with a batch size of 256, a learning-rate
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Algorithm 1 DiffBED: BED with Information Guided Diffusion
Input: BED setup: prior p(f); likelihood p(y {. experiment steps K
Input: Diffusion: reference score model stri; SDE steps T;; guidance scale a
Input: Inference: partiele count N: partiele filter;
Output: Designs çl:K, observations y 1: particles (0(K) 1N
Jn=1i
p(0): set E + 0, y 1.0 0. Initialize: draw {0 ).
2: for k = .. K do Diffusion-based design sampling 3: Er N/0 T)
Sequentially design and each experiment
Initialize noise
4: for t = T.T I...., 1 do
5:
9: V (Eo((E(()()) f SDEstep(Er, (e
Estimate EIG gradient using (0% |)
6:
SDESolver step
7:
end for
8:
Set design 5h + Eo
Run experiment and update posterior
9:
ye y p(y 0r, gh)
10: Elik + e elik-1 U (5"), yli +- ylik-1 {/"}
{0!h) ParticleFilter (foh ), elik yl:k)
11:
12:
end for return El:K, y (0/²))
13:
of 1, and with SGD as the optimizer. We utilise an Ordinal-Logi model with an underlying reward re(E) (E) - cos_sim(simccr(())
B DIFFBED DETAILS
This section contains the algorithmic details needed to implement Di DiffBED in practice. In Algorithm provide pseudocode which describes how DiffBED is applied end-to-end for (sequential) BED problems.
B. REFERENCE MODELS
For each experiment, we require a reference diffusion model Prer(E) whose samples produce reason- able designs for the problem at hand. We detail our specific choices for each dataset here.
MNIST We use the training script provided in the PyTorc codebase provided by Song et al. (2021)² to train unconditional MNIST diffusion model. We residual block per level) with VP-SDE with linear noise schedule B(t) = Bunn + t(3max Buin)
NCSN+ UNet (64 base channels, one
t e [0, 1]. i.e., f(x t) z (t) x and g(t) / B(t) (6min = 0.01, 3max 20). We train for 500k iterations, with EMA (0.999) and batch size of 256, using the Adam optimizer (Ir 0.0002, with gradient clipping at norm- 1.0).
CelebA and Zappos For the higher dimensional datasets, CelebA (Liu et al., 2015) and Zappos (Yu & Grauman, 2014), we leverage the Hugging Face di diffusers library", which provides standardized pipelines for training, inference, and sampling of diffusion and latent diffusion models. For CelebA, we use pre-trained latent diffusion model (Rombach et al., 2022) checkpoint." For Zappos, we use a fine-tuned version of Stable Diffusion v1.5 (SDv1.5).
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shoe-dataset
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B.2 SAMPLING
We now turn to the details involved in sampling from pE() using Equation (15). In particular, Shen al. (2024) considers the shortfalls of training-free guidance of diffusion models and leverage ideas from optimization literature to mitigate them. We find that Polyak step-size parametrisation of the guidance scale is beneficial in finding favourable trade-off between the informativeness and realism of designs. Namely, this considers a time-dependent guidance scale as multiplier of the EIG gradient estimator, which we denote as 7/ for brevity, during the reverse-process
(Ep t)ll 1mell
att) =
(17)
Across all experiments, we use the to the ancestral/DIDPM sampler. We provide further dataset-specific sampling hyper-parameters below. We use uniform time-steps on all datasets, with 500/250/100 steps on MNIST/CelehAA/Appos respectively. The choice of the 1j is an empirical one, determined by the robustness of the reference diffusion model (Ye et al., 2024). We set this parameter by visually inspecting small set of samples for increasing values of 17, setting the maximal value that still consistently produces high-fidelly images. We 7 0.0375, 0.10 for CelebA/ZZapoos experiments, and present example samples produced at this guidance scale in Figure lla and Figure 6.
discretization of the reverse SDE, equivalent
As SDv1.5 is text-conditioned model, of interest for the Zappos task: 'studio product photo of a footwear, et white te ba background, high detail'' To avoid artefacts, we also the following negative prompt: 'blurry, low resolution, watermark, deformed''.
the following prompt capture the data-distribution
B.3 NUMBER OF FUNCTION EVALUATIONS (NFES)
We report cost in terms of network function evaluations (NFEs), counting a single forward pass through either the diffusion model or the design-embedding network as one NFE. While the embed- ding network is substantially cheaper than the diffusion model in our experiments, we ignore this difference, which favours the Rank (Diffuse) baseline, and treat both unit-cost for simplicity.
DiffBED At each reverse-diffusion step we (i) evaluate the diffusion score (1 NFE), and (ii) estimate the EIG, which in our image experiments is dominated by single forward pass through the
network (1 NFE). To form the information -urioonne term, we additionally back proppappee through both networks; we approximate the cost of cach backward pass as 2x its corresponding forward pass. Therefore, over the reverse process, we incur 4K NFEs.
Rank (Diffuse) Baseline With N candidate designs, this baseline requires running a K-step reverse process for each candidate (KN NFEs), plus an additional EIG estimate per candidate (N NFEs), for total of KN N NFEs.
Compute Normalization When comparing Rank (Diffuse) to Di FFBDD, we match compute by choosing N such that K N + N as 4K (for large K, this is well-approximated by N as 4). In practice, we use = 5 (rather than N z 4) to err on the side of over-allocating compute to the baseline.
C POSTERIOR INFERENCE
We now present details on how we conduct inference on the embedding space during active experi- mentation. In search problems, the encoders are trained with cosine-similarity objective, both our likelihoods and the geometry of the problem depend only on the direction of 0, not its scale, Similarly, in preference elicitation settings, often want to learn normalized preference weights 6 in order to allow for explicit control and regularisation over the sharpness of the preference distributions, for example through scaling hyper-parameter.
In such settings, although lives in TRP, the unit-length constraint removes one degree of freedom, leaving intrinsic dimension of D 1. Accordingly place uniform prior the unit sphere SD-1 = {0 E R ||0|| = 1} the (D 1)-dimensional manifold of D-dimensional vectors of length one. We then explicitly approximate the posterior the unit sphere.
Another alternative learn weights that sum one.
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Particle-Based Inference At the start of the experimentation draw an i.id. set of particles ( Fi=r Unif(sD-1) to represent this prior. At each experiment index k after observing an outcome ys design Éu. we update particle weights according to the likelihood
logw;" (k) = log w (l-1)) + logp(y" 1 (00-111,,, ,
Weights are normalized and particles are resampled via multinomial resampling to prevent degeneracy (Doucet et al., 2001), yielding empirical posterior approximation {0[").
To maintain diversity and ensure that the particle cloud accurately tracks the true posterior on the sphere, we rejuvenate the particles by applying projected unadjusted Langevin algorithm (ULA) SD-1;
0 Normalize (o (
C PoVa P log (0) + Vt Pon)
where Pe = I - 00 projects gradients and noise onto the tangent space T and 17 (0, I). This step can be viewed as an unadjusted discretization of the Riemannian Langevin diffusion on & Calderhead, 2011; Patterson & Teh, 2013), where the drift term is the gradient of the full current posterior T& (0) To (0) 1_=pp(y) A, ("), so that each move incorporates all experimental observations up and including experiment index k.
Computational Cost As the log-likelihoods are parametric functions of simple vector products, iee. cosine-similarities, between and encodings of previous designs, both resampling and Langevin steps are very efficient." ? Crucially, resampling and Langevin steps do not require expensive neural network evaluations per 0 particle. For all experiments, we leverage N = 10th particles, take 100 Langevin steps, and have step-size dimensionality D = 32, 64 has costs = 122, 244 MiB of memory, which is a negligible overhead on modern GPUs.
10 10-4 Note that the cost of storing N 10 particles of
Decoding from Latent Space We can also recover 0 in full image space from latent posterior samples. The simplest approach nearest-neighhour retrieval from large pool. Instead, to obtain the posterior samples shown in Figure 2, we guide diffusion model over 0 (which is also image-valued our search experiments) to target the distribution
p' (0) x p(0) exp (a x cos (imtenate::: E(O)))
(18)
Intuitively, this synthesizes image-space 0 whose embedding E()) matches a latent posterior particle Oratent under cosine similarity. To sample from p" (0) in Equation 18, we use approach that is directly analogous to that in Section 4.2, now guiding the diffusion model to sample A.
D LOCATION FINDING
In this section we present additional details for source location finding experiment in Section 6.
Interpretation of Data-Generating Mechanism many real-world cource-finding tasks, such as localizing radio beacons, chemical or radiation leaks, acoustic emitters, the assumed physical model (e.g., an inverse-squee squure decay) is only accurate in regions where the environment is simple and well-behaved. In such areas, such open or unobstructed areas, the measurements should typically follow the expected model, Pmodel- However, when the sensor moves into more complex environments, such areas with obstacles. turbulent airflow, or reflecting surfaces, the underlying physics changes, producing systematically different observations. Our mixture formulation captures this spatially dependent model fidelity by allowing designs inside certain regions follow the assumed model, while those outside follow an alternative, unknown likelihood, Pood Effectively modelling the physics outside of the simple case where Pmodel is accurate may not be feasible. If this is the case, we may wish to find informative design, whilst encouraging adherence to design prior, where we can trust our ability to model the data settaagnenating process.
Hyperparameter Settings Following Foster et al. (2021), we set D = 2, = = 02 = m 10 4, = 10-1 o = 0.25, and design K 30 sequential design optimizations. For DiffBED
Note that embeddings of designs/design sets can be cached, and such, just needs to be computed once. For the of the roll-out, it can be shared across all particles for resampling and Langevin-step computation.
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and Entropy, with MNIST, a VP-SDE with linear noise schedule ((t mmin t(3maxx mmin) E [0, 1), i.e., f(x, 2 ((t) and gt) /tt) (Bmin 0.01, 8max 20)
Misalignment We define the well-aligned region, E", to be eight circles with radii equal to 0.4, and each circle centred the circumference of the unit circle (such that the spacing between the circles is even). This geometry is inspired by the eight Gaussian dataset, commonly used for demonstrating generative models on simple datasets. For Pood, we use the same form and parameters as the aforementioned Pmodel but with a1 = Q2 = 0.5. As such, in misaligned regions, the signal mean, p(0, E) is systematically lower. We stress that in real-world scenarios, we have very limited knowledge of Pood, and hence cannot write down an explicit Pyru0yy
Design Strategies For an implicit design prior Pref, diffusion model trained to sample a Gaussian mixture model (GMM) with eight Gaussians with evenly-spaced means on the unit circle and diagonal covariance matrices (Σ x² /2; a = 0.1) could be used. Note that this design prior assigns high mass to regions in E and thus reflects our preferences towards areas of design space that exhibit lower misalignment. For design prior that is a GMM, the time-dependent score Ve, log Pt (E(E)) is available analytically 8, As such, we simply use the analytic time-dependent score in the reverse process with Di FEED. For the Rank variants and Random, we also sample candidate designs from this GMM. BED, as in the main body of the paper, is unconstrained, gradient-band optimisation of designs. In this experiment, the observation y is continuous. As such, use the prior contrastive estimator (PCE) (Foster et al., 2020) for estimating the EIG and its gradients.
Inference For all strategies, perform posterior inference using particle-basee basee ULA scheme as described in Appendix C, omitting the projection step, with N = 10 particles.
Evaluation We compute the incremental EIG of the chosen design at each iteration using the pCE estimator using N = 9 000, .M = 110 posterior samples (taken from the 10 inference particles). The model exhibits non-identifiability with respect to the ordering of the two sources, 0, and 02 during posterior sampling. As such, the correspondence between estimated and true sources may be swapped between samples. To address this when computing the L2, we evaluate both orderings of each posterior sample and use the ordering that yields the lower error. We average over 25 roll-outs with different random seeds and present our results in Figure
In addition to the quantitative results presented in the main body (Figure 3), we present an aggregation of the experimental designs, across rollouts, for each design strategy Figure 8
DifBBE
Rank (1000)
Random
BED
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Figure 8: Designs aggregated across all iterations and experimental rollouts (25 seeds x 30 iterations) for 2D location finding. Di Diff, Random and Rank all leverage the implicit design prior in different ways to produce designs from regions where there lower model misalignment. On the other hand, BED produces designs by only maximising the HIG, producing designs that lie in regions where there is greater misalignment.
As our design prior is GMM, the time-dependent score Vs, (o()) under the variance-preserving diffusion process is available in closed form. Specifically, the forward process is & = vas Eo + of the GMM,
vI are, g Io and marginal density time is a Gaussian-convolute Pr(E)) _ km TT (g:; Vorue, E+ (1 -)) which remains mixture of Gaussians with inflated covariance. Hence the score has trivial analytic expression.
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DifiBED
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Figure 9: Incremental EIG (under Pmodel) each experiment iteration (left) and average L2 error between posterior samples and ground truth locations (right) for a larger range of size of candidate sets.
E ADDITIONAL. IMAGE EXPERIMENTS
E.1 CELEBA: ACTIVE PREFERENCE ELICITATION
In addition to the search experiments in the main body, we present an example of active preference elicitation on CelebA. The search experiments in the main body focus on recovering single observ- able parameter 0, often using designs that live in the same space as 0 itself (e.g., the image search motivated by the criminal sketch problem). contrast, active preference elicitation concerns learning user's latent preferences, such set of preference weights over interpretable attributes styles.
This problem class widespread, with motivating examples ranging from recommender systems to personalization. For instance, dating platform may wish to recommend profiles that user is likely to engage with. A common modelling assumption that a user's preferences can be summarized by weights over distinet, interpretable features (e.g., whether the image depicts glasses smile). Under this view, preferences can be inferred from pairwise comparisons, where the user indicates which of two candidate profiles they prefer.
Concretely, for this experiment, we take 0 as a unit-normalised vector which each element is a preference weighting for binary CelebA attributes. We Bradley-Terry (BT) response model, in which designs are pairs of images. We parametrise the latent reward as being proportional to the dot product between the preference vector and vector of classifier probabilities that each attribute is present for each image in the pair. See Appendix A for additional experimental details and Appendix for details about the inference.
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Figure 10: EIG and cosine similarity for preference elicitation CelebA. Designs consist of image pairs with binary preference responses. Standard BED yields EIG values comparable to random selection and struggles to identify the true preference vector (low cosine similarity). while Diff maintains higher cosine similarity and more informative designs.
As shown in Figure 10, DiFfBED achieves consistently high EIG designs and substantially outper- forms both the standard BED and random baselines by producing much higher cosine similarities.
Interestingly, the EIG performance of the standard BED baseline substantially lower than D. DiffrED and the other baselines. This suggests that gradient-based optimisation is struggling here, unlike in the search experiments, where BED produces consistently high-EIG designs, albeit totally unrealistic ones. A likely reason is that, in this setting, the EIG is defined through classifier trained for discrete prediction, whose mapping from input to output is dominated by saturated confidence regions and sharp decision boundaries. In such regimes, gradients with respect to the input be poorly conditioned, often near-zero or highly variable, making it difficult for gradient ascent to reliably improve the design objective.
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(a) DiEtBED designs.
(b) Entropy designs.
Figure 11: Example designs for the CelebA search problem.
By contrast, the reference prior in DiffBED helps guide optimisation toward sensible designs, assisting the method locating regions of the design space with high EIG even when the EIG signal itself is weak or noisy. While Di E EEBD again outperforms Entropy on this problem, Rank slightly outperforms This likely relates to the poor performance of BED in this task, and to the quality of EIG gradients when the likelihood is parametrised by discriminative classifier rather than smoother, more continuous encoder. We thus find that Rank provides a useful variant of DiffBED for setups with more discrete features, but is less helpful when simple sampling from (r) is insufficient to generate good candidate designs.
E.2 CELEBA: INTORMATION- SEARCH
We present below additional experiments for information- search CelebA.
Example DitIBED Designs: CelebA Figure 1la shows 100 example images generated by DiffBED and Figure 1lb shows the same for Entropy. This serves qualitative evaluation of our designs. Both are similarly high-quality images as they leverage the same underlying diffusion model, although with different objective functions for guidance. On the other hand, the designs pro- duced by standard BED (Figure 12) are imperceptible from pure noise, despite their high EIG values.
Ablations In Figure 13 present results across the two
values of the likelihood temperature parameter - = {25, 50}. in addition to the value of - 10 used for CelebA in the main body of the paper. Larger values of r indicate less noise in the observation process, i.c., more informative outcomes, We see that larger - indeed leads to larger EIG values and a larger gap to the random baseline.
Here, we also present the performance of the naive BED baseline under data simulated from the as- sumed model which we call BED (assumed). That is, we sample y ~ p(y 6, <) from the misspecified model likelihood, with no adjustments to the fact that the resulting designs may be meaningless. We see that BED (assumed) achieves both high EIG scores and cosine similarities in this case. However, the designs produced by BED in this case imperceptible from pure noise (Figure 12) and could not be used in a real-world experiment. As soon as we sample data y from a more realistic likelihood which returns uninformative data when the designs are pure noise, the cosine similarity of the naive approach (BED) drops to near zero, indicating a failure to determine the correct 0.
In second ablation, study the effect of the number of the candidate designs considered in the Rank method. We plot the performance with N 100, and N 10000 candidate designs, alongside the N 1000 set-up used in the main body of the paper. See Figure 14. Unsurprisingly. the
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Figure 12: Example standard BED designs for the CelebA search problem.
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Figure 13: EIG and cosine similarity values for CelebA on the search problem, where outcomes are top-2 ranks the images in the set four design images. We now vary the value used in the likelihood. Means are plotted + one standard error.
performance of this baseline is a monotonic function the pool size. However, increasing the pool size also comes with additional costs, especially when the pool is itself generated from model, in which case N 10000 would be significantly more time consuming than Di FFBED.
E.3 ZAPPOS
Example DifTBED Designs: Zappos We present 100 example designs produced by DiffBED and standard BED on the Zappos discrete rating problem. See Figure 15b and 15a.
Ablations We additionally present in Figure 16 results for 10 levels of discrete ratings, rather than N = 5 used in Section 6.3. Intuitively, might expect that more fine-grat fine-grained rating would be more informative. Indeed, comparing against Figure 7, using N = 10 yields slightly higher cosine similarities.
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Figure 14: EIG and cosine similarities the number of candidate designs consider by the Rank baseline in the CelebA search problem. Means are plotted + one standard error.
(a) Standard BED designs.
(b) LIE designs.
Figure 15: Example designs for the Zappos discrete rating problem.
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Figure 16: Quantitative results on the Zappos dataset, where designs are single images and outcomes are discrete ratings now on scale from 1-10. Means are plotted t one standard error.
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Reviews:
[{"review_id": "4DoImuPbKp", "reviewer": "Reviewer_tuUX", "summary": "This paper presents an approach to apply diffusion models to propose informative and plausible designs for Bayesian adaptive experimental design in high-dimensional design spaces. The paper shows that, in such settings, likelihood model misspecification can severely misguide BED algorithms towards designs which have an apparent high expected information gain (EIG), though due to errors in the likelihood model, leading traditional methods to produce no longer meaningful designs in high dimensions. To mitigate that, the proposed method employs pre-trained diffusion models whose samples are guided by an EIG-based gradient estimator towards designs which are informative for the given task without the need to retrain the diffusion model. Experiments are presented on high-dimensional experimental design problems involving images.", "questions": "Please, see weakness points above. In addition, I have the following more specific questions.\n\n* Have other high-dimensional experiment settings been considered, beyond images? As far as I understand, diffusion models could also be applied in lower-dimensional settings and compared against other BED baselines in more traditional problems. Some synthetic problems can have their dimensionality adjusted in ablation problems to show how the performance of standard methods potentially degrade as the dimensionality increases, while hopefully DiffBED maintains reasonable performance levels.\n\n* Did each experimental trial have a different target image in Sec. 6.1? Or was the same image used across each experiment, with the different random seed only affecting optimisation behaviour?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The paper is mostly well written and follows a clear structure which is relatively easy to follow.\n* The proposed method seems relatively simple to implement within modern generative modelling frameworks.\n* Some of the principles and insights in this paper may be applicable beyond its setting, such as the presentation on the issues with misspecification in BED, how a prior over feasible designs can help mitigate these issues, and how to apply pre-trained diffusion models to design tasks without a need for retraining.", "weaknesses": "* In Sec. 3, it is not clear how the decomposition of the EIG from Eq. 5 to 6 was derived. Eq. 5 was derived using the alternative formulation of the TEIG in terms of $\\theta$, instead of $y$, which was the one presented in Eq. 4, making things confusing. Eq. 6 seems to have been derived by adding and subtracting TEIG from the model's EIG, but why the step in Eq. 5 was necessary is unclear.\n* It is not explained how Eq. 11 was derived. I believe that might require some background in diffusion models, though such a derivation should at least be found somewhere in the appendix, given that the EIG guidance term is a crucial contribution from this paper.\n* Experiments are presented on image design tasks, which escape traditional problems in experimental design, making it difficult to assess the impact of the paper outside this context. Despite the complexity of optimisation and sampling in high-dimensional design spaces, the probabilistic models in these experiments seem reasonably simpler than traditional models found in science and engineering applications where BED typically finds its applications. Hence, I'm unsure of this paper's impact.\n* The presented performance plots show that, besides the gradient-descent BED baseline, the proposed DiffBED's performance is mostly very close to the performance of simpler baselines. Yet, I reckon that std. deviations, which I interpret as the shaded areas around the curves, are quite small as well. Therefore, the practical significance of this paper's contribution remains unclear.\n* I'm also unsure about the claim in Sec. 5 that \"the first to identify that model misalignment is not constant across design space and show the potential for reward hacking\". Prior work in BED has discussed issues related to model misspecification and their effect on design optimisation, such as Foster et al. (2025), though to a different extent. In addition, the issue of model mismatch as a function of the designs is explicitly modelled in, e.g., Bayesian calibration frameworks by the model discrepancy/error term (Kennedy & O'Hagan, 2001), which have been recently applied to BED (Oliveira et al., 2024; Sürer et al., 2024). Additional references are listed below.\n\nMinor:\n* A few typos are present throughout the text, which require careful revision.\n* Eq. 10 is missing a time differential $\\mathrm{d}t$ next to the term in brackets.\n* I believe it should be $\\xi_t$, instead of $x_t$, in the inline equation on line 244.\n\nReferences:\n* Kennedy, M. C., & O’Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(3), 425–464.\n* Oliveira, R., Sejdinovic, D., Howard, D., & Bonilla, E. V. (2024). Bayesian Adaptive Calibration and Optimal Design. 38th Conference on Neural Information Processing Systems (NeurIPS 2024).\n* Sürer, Ö., Plumlee, M., & Wild, S. M. (2024). Sequential Bayesian experimental design for calibration of expensive simulation models. Technometrics, 66(2), 157-171.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "idwUNo2Xst", "reviewer": "Reviewer_MFdK", "summary": "This paper addresses the problem of scaling Bayesian Experimental Design (BED) to high-dimensional design spaces by first identifying a critical issue: directly optimizing Expected Information Gain (EIG) in high dimensions exploits model misspecification, producing unrealistic designs (e.g., noise images) where the likelihood is overconfident. The authors propose DiffBED, which constrains design optimization using a diffusion model as a reference prior over feasible designs, sampling from a distribution proportional to $p_{ref}(\\epsilon) \\cdot \\exp(EIG(\\epsilon)/\\alpha). Designs are generated via information-guided diffusion, combining the diffusion model's score function with EIG gradients in the reverse SDE. The authors conducted experiments on image-based tasks, and DiffBED generates realistic and informative designs in high-dimension space, while standard gradient-based BED fails by producing noise despite high model EIG.", "questions": "1. Please see the comments in Weakness part.\n\n2. Could the authors provide more details on the BED baseline used in the experiments? I would suspect that the main computational bottleneck is the EIG gradients calculation, so how much does the proposed method cost more than the BED baseline?\n\n3. It seems that the Rank baseline is highly competitive in the conducted experiments, can the authors discuss in more detail?\n\n4. The proposed method depends on high-quality pre-trained diffusion models and encoders, which are feasible for vision but limited in other domains. Could the authors discuss the feasibility of applying DiffBED beyond vision (e.g., molecules, audio, text, tabular data), what happens when good diffusion models might not exist, and discuss when DiffBED is preferable over simpler pool-based approaches like Rank?", "limitations": "", "rating": 4, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The problem studied in this paper is well-motivated, and the authors clearly justified that EIG optimization inherently seeks regions where the likelihood is overconfident, identifying model misspecification as the fundamental barrier to scaling BED.\n\n2. The reward hacking analogy well motivates the approach, and by incorporating pre-trained diffusion models as reference priors, the proposed method prevents reward hacking while maintaining high informativeness.\n\n3. Experimental results demonstrate that DiffBED is able to scale on high-dimensional settings.", "weaknesses": "1. The proposed method is highly dependent on having a high-quality, pre-trained diffusion model for the design space. This does not fully solve the high-dimensional problem as shift it from needing a perfect likelihood to needing a perfect generative prior. It would be great if the authors could elaborate more on this part.\n\n2. The proposed method is computationally expensive as it requires running a full, guided reverse-diffusion process for each experimental iteration.\n\n3. I think the authors should position the method as a hybrid, not a purely Bayesian one. It combines principled Bayesian inference (for $\\theta$) with a pragmatic, regularized optimization (for $\\xi$). The design objective $p^{*}(\\xi)$ introduces $p^{ref}(\\xi)$ as an external regularizer not derived from the original generative model.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "G2rhCEdS6C", "reviewer": "Reviewer_nkQr", "summary": "This paper introduces DiffBED, a Bayesian experimental design method for high-dimensional design spaces that uses a pretrained diffusion model as a prior over feasible designs. The approach guides the reverse-diffusion process with gradients of expected information gain (EIG), producing proposals that stay on the data manifold (realistic) while remaining highly informative for learning the latent target. The authors argue that naïvely maximizing EIG in high dimensions can “reward-hack” likelihood misspecification; DiffBED mitigates this by sampling from an EIG-tilted prior rather than optimizing EIG directly. On image-level tasks—including 512×512 shoe designs—DiffBED outperforms standard BED and several strong baselines.", "questions": "1. Did you try a direct EIG optimizer that stays on the data manifold (e.g., trust-region steps or EIG + prior penalty)? What’s your intuition for how it would perform vs. DiffBED?\n\n2. How sensitive are performance and diversity to $\\alpha$?\n\n3. On multi-peak landscapes for $p_{ref}(\\theta)$, do you see mode collapse when $\\alpha$ is small?\n\n4. What happens when the prior is biased or domain-mismatched—does it still produce meaningful designs?\n\n5. For continuous y, how would you estimate EIG, and which gradient estimator would you use (just a brief idea is fine)?\n\n*** Duplicate word *** \n\nline 222, by solving time-reversal of Equation (9)", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper clearly shows how naive EIG in high-dimensional settings can suffer from likelihood misspecification, which makes staying on the data manifold meaningful.\n\n2. Exponential tilting of a diffusion prior is a clean way to sample realistic, informative designs—no extra training required.\n\n3. This method uses a pretrained diffusion model, so there’s no retraining at every step which is time consuming for sequential BED.\n\n4. This method works on large images (512×512) and outperforms standard BED.\n\n5. This method improves the similarty to $\\theta_{true}$ , which indicates true target recovery.", "weaknesses": "1. The paper doesn’t compare against a simple constrained EIG optimizer that stays on the data manifold (e.g., trust-region steps or directly maximizing EIG with a prior penalty). Without that apples-to-apples baseline, it’s hard to tell whether the gains come mainly from enforcing feasibility or from sampling the EIG-tilted prior itself.\n\n2. Exponential tilting can collapse to a single mode on multimodal landscapes, and picking a good $\\alpha$ is non-trivial because it trades diversity against feasibility.\n\n3. The method leans on a strong pretrained diffusion prior. If an appropriate prior doesn’t exist or is domain-mismatched, it may be inapplicable, and tilting can’t add mass where the prior has zero mass.\n\n4. Results focus on discrete outcomes; if y is continuous, EIG estimation and gradients are harder.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)