Generating Informative Samples for Risk-Averse Fine-Tuning of Downstream Tasks
Authors: Heasung Kim
Taekyun Lee
Hyeji Kim
Gustavo De Veciana
Venue: NeurIPS 2025 spotlight ()
Keywords: Generative models
data augmentation
score-based generative models
risk
importance sampling
wireless communications
applications
Primary area: general_machine_learning
TL;DR: A novel risk-averse training framework that leverages score-based generative models for data augmentation tailored to Conditional Value-at-Risk minimization

Abstract: Risk-averse modeling is critical in safety-sensitive and high-stakes applications. Conditional Value-at-Risk (CVaR) quantifies such risk by measuring the expected loss in the tail of the loss distribution, and minimizing it provides a principled framework for training robust models. However, direct CVaR minimization remains challenging due to the difficulty of accurately estimating rare, high-loss events—particularly at extreme quantiles. In this work, we propose a novel training framework that synthesizes informative samples for CVaR optimization using score-based generative models. Specifically, we guide a diffusion-based generative model to sample from a reweighted distribution that emphasizes inputs likely to incur high loss under a pretrained reference model. These samples are then incorporated via a loss-weighted importance sampling scheme to reduce noise in stochastic optimization. We establish convergence guarantees and show that the synthesized, high-loss-emphasized dataset substantially contributes to the noise reduction. Empirically, we validate the effectiveness of our approach across multiple settings, including a real-world wireless channel compression task, where our method achieves significant improvements over standard risk minimization strategies.

Generating Informative Samples for Risk-Averse Fine-Tuning of Downstream Tasks
Heasung Kim, Taekyun Lee, Hyeji Kim, and Gustavo de Veciana
Department of Electrical and Computer Engineering The University of Texas Austin Austin, TX 78712 (heasung. kim, taekyun, hyeji, deveciana) edu
Abstract
Risk-averse modeling is critical in safery-sensitive and high-stakes applications. Conditional Value-at-Risk (CVaR) quantifies such risk by measuring the expected loss in the tail of the loss distribution, and minimizing it provides a principled framework for training robust models. However, direct CVaR minimization re- mains challenging due to the difficulty of accurately estimating rare, high-loss events panticclaalllllrlyy extreme quantiles. this work, we propose a novel train- ing framework that synthesizes informative samples for CVaRR optimization using score-based generative models. Specifically, we guide a diffusion- based generative model to sample from reweighted distribution that emphasizes inputs likely to incur high loss under a pretrained reference model. These samples are then in- corporated via loss-weighted importance sampling scheme to reduce noise in stochastic optimization. We establish convergence guarantees and show that the synthesized, high-loss-emphasized dataset substantially contributes to the noise reduction. Empirically, we validate the effectiveness of our approach across mul- tiple settings, including real-world wireless channel compression task, where our method achieves significant improvements over standard risk minimization strategies.
Introduction
Risk-averse learning has become increasingly relevant high-stakes applications where robustness to rare but costly failures is critical. In those domains, models must not only achieve strong average-case performance but also avoid catastrophic errors on atypical inputs. widely adopted risk measure for capturing such sensitivity is the Conditional Value-at- -isk (CVaR). which focuses the expected loss in the worst-performing (1 - 3) fraction of the input space (Rockafellar and Uryasev] 2000). making it well-suited for applications requiring robustness guarantees, e.g., large language models, system scheduling, control, medical, wireless communications, and more (Chaudhary et al. 2024
Tan et al. 2017 Ahmadi et al. 2022 Chan et al. 2014 Yang al. 2022).
Despite its appeal, minimizing CVaR remains challenging in practice. As the quantile level approaches one, loss contributions become dominated by rare, high-risk inputs that are unlikely to be observed through standard sampling from the data distribution. Without adequate coverage of these tail events, naive Monte Carlo (MC) methods yield high- high-variance estimates of CVaR and inefficient optimization, ultimately limiting the reliability risk-averse training.
"Corresponding Author.
Source code: https://github.coo downstream tasks
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

p(x)
((x) & cp(((0o; x)) p(x)
Generative model
Sample from g(x)
high
CVaR
Pretrained task model 0,
High-loss inducing samples
Risk-averse model Or
Figure 1: System overview. A score-based generative model is guided using the loss values from pretrained model sample high-loss inputs for CVaR optimization.
Recent advances in generative modeling offer new opportunities address these limitations. In particular, score-based generative models enable expressive and controllable sampling from complex distributions, and have shown promise in tasks ranging from data augmentation to density estimation. Concurrently, pretrained task models are becoming widely available and serve as informative priors for task performance. These developments motivate fundamental question: Can we actively generate training inputs that are more informative for CVaR optimization?
In this work, we propose novel framework that integrates pretrained (reference) models and generative models to synthesize informative samples for risk-averse training. Our key observation that inputs which induce high loss under pretrained model are highly beneficial for risk-averse model training. This motivates data generation strategy that explicitly targets failure modes of the initial model and uses them to guide risk- awsre training more effectively.
To realize this idea, we develop a method that uses pretrained loss values to guide a score- generative model toward reweighted sampling distribution that emphasizes high-risk inputs. Our approach leverages recent advances in training-free guidance for diffusion models, allowing the generative process to be steered without retraining (Chung et al., 2023; Yu et al. [023 Kim et al.] 2025c). The resulting samples are explicitly biased toward regions where the model is likely to Tail and are used to perform CVaR minimization via aepootaacc-weighhee optimization. The main contributions of this work are summarized as follows.
Framework Design. We propose novel risk-averse learning framework based loss-guided generative importance sampling. As illustrated in Figure [ our approach proceeds in two stages: (i) a pretrained model is used to guide score-based generative model to sample from reweighted distribution that emphasizes high-loss inputs: (ii) these samples are then used for CVaR minimization via importance-weiggted training, resulting in improved robustness and reduced training noise.
Theoretical Analysis. We provide convergence analysis for our framework and show that, under mild assumptions, generating samples from high-loss regions provably reduces the noise of the CVaR optimization process.
Empirical Validation.
We empirically validate our method in both synthetic and real-world settings. In a controlled regression task with highly imbalanced modes, the proposed method successfully synthesizes rare, high-loss samples that are critical for minimizing tail risk. In a real-world appli- wireless channel state information (CSI) compression- our method consistently improves CVaR performance in the high regime, compared to existing robust and risk-minimization baselines.
To the best of our knowledge, this is the first work that leverages generative models perform risk-averse learning by targeting high-loss regions via loss-guided importance sampling.
2 Related Work
Risk-Averse Learning and Conditional Value-at-Risk. Risk-averse learning seeks to prioritize robustness over average-case performance, especially in high-stakes settings where rare but severe failures are unacceptable. A widely used risk measure this context CVaR (Rockafellar and Uryasev 2000), which quantifies the expected loss in the (1-3) (1-33--wwrrr --orststtt portion of the input distribution. Due to its ability to explicitly penalize high-loss instances, CVaR has been adopted in broad range of applications, including finance, credit, operational risk management, robust control in wireless

---

communications, large language models, and more (Alexander et al. 2006; Andersson et al. 2001 Filippi et al. 2020 Yang al. 2022; Chaudhary al. [024]] Chow and Ghavamzadeh 2014).
However, training with CVaR objective is notoriously challenging due to the high variance in empirical estimates, particularly when targeting extreme quantiles (Troop et al. 202T].
Importance Sampling for Risk Measures and Optimization. Importance sampling can be utilized for improving the variance of risk estimation, particularly when rare events dominate the objective. Prior works have explored its use in CVaR estimation and optimization (Bardou et al.) 2009; Deo and Murthy 2021 He et al. 2024a),, including sampling-base bbstn gradient estimators based on likelihood ratios Taaar et al. 2015). However, these approaches typically operate on a fixed dataset and focus on reweighting existing samples to reduce estimation variance.
Our method introduces a fundamentally new perspective: we utilize generative model to directly synthesize importance-weighteed samples. Under the availability of generative model, we guide the sample generation process toward high-loss regions using pretrained model losses. This enables us to reduce the noise of CVaR optimization while expanding the effective support of the training distribution.
Generative Models for Data Augmentation and Downstream Task Learning. Recent progress in generative modeling, particularly in diffusion and score-based generative models, has enabled high- fidelity sample generation and accurate distribution approximation (Chen et al.) 2024; Wang et al.) 2024b). These models have been successfully applied across diverse domains for data augmentation, including load forecasting (Xu and Zhu (024), medical imaging (He et al,, 2024b), and audio synthesis (Bahmei et al. 2022). Recently, generative models are increasingly used to augment training datasets with specific purposes (Zheng et al. 2023), e.g., enhancing semantic diversity
(hhivashankar and Miller [023] Trabucco et al. 20033) generating label-specific instances (Shao)
al. (019), and bridging distributional gaps between training and test data (Wang et al.) (2024a).
Scope and Distinetiveness of the Proposed Approach. While prior work has primarily leveraged generative models to enhance generalization by enriching the diversity of training data, our approach adopts different objective: synthesizing samples that are explicitly informative for risk-sensitive training. Rather than uniformly augmenting the training distribution, we concentrate generation toward high-loss regions- thhoes most relevant for CVaR minimization. This targeted generation paradigm aligns directly with risk-averse learning objectives, offering a principled and efficient path toward robust model training.
3 Preliminaries and Problem Formulation
Recent advances in generative modeling, particularly score-based generative models, have substan- tially improved the quality and controllability of synthetic data generation. A key strength of the score-based generative models lies in their ability support guided sampling, where samples be drawn from a distribution that is shifted or reweighted relative to a base distribution. In this work, we leverage this capability to generate rare, figh--loss-ndduciie samples that are underrepresented in standard datasets but critical for risk-sensitive objectives. As we will show, synthesizing such samples provides both theoretical and practical advantages in CVaR minimization.
3.1 Score-based Generative Models and Training-Fres Guided Sampling
Let X e dR be random variable with density p(x), where x denotes a realization. A generative model seeks to approximate p(x) or its associated score function V, log p(x) to enable efficient sampling from the underlying distribution. A key innovation of the recent score-based generative models is to model the score function not directly on p(x). but on noise- peritsepertureed data distributions (x(x) indexed by a continuous-timg
parameter E [o. T]. This enables the data generation process to be formulated as a stochastic differential equation (SDE), which has been shown to enhance both training stability and sample quality (Song et al. 2021 T). The perturbed distributions are modeled via the Itō SDE:
1) dt + all) dW dxP = =(X)
X p(x),
(1)
3

---

where f Rd x [0, + Rd is the drift term, (tt) |0, T] + R the diffusion coefficient, and W(e) is a standard di -dimensional Brownian motion. The marginal distribution of ( is denoted Px(x), and the initial distribution po(x) corresponds to the data distribution we aim to model.
Given access to the time-indexed score Vx log (xx), samples from p= Pu can be obtained by solving the reverse-time time SDE (Anderson, 1982):
dxP (4) = (f(x)) (f(X))) (1) V log (o)) dt + (t) (Q)))
where W(e) (e) denotes reverse-time Brownian motion. Sampling is typically initialized from a simple prior such as standard Gaussian pr (x) for large T, and trajectories are integrated backward to recover X Po- For notational simplicity, scalar-vector multiplication denotes elementwise scaling.
Beyond sampling from the base distribution p(x), recent advancements in the score-based generative models allow sample generation from modified target distributions of the form (xx) x w(x)p((x), where w(x) task-specific importance weight. While classical approaches such the cross- entropy method (CEM) and fine-tuning of generative models require retraining to realize such reweighted distributions, training-fres guidance techniques for the score-based generative models enable approximate sampling from y without modifying the base generative model. These methods exploit the fact that, under the same SDE dynamics in I if a process begins from g(x) = qo(x) oc w( (x))p(x) instead of p as dxx),) f(X t) dt + (t) dW (1) with X
~ ===q=oo qo. then its marginal
Gt. such that x (1) ge satisfies (x( x px(x) Ex,
w X (0)) where p(- ( = x)
(0) ~p( Xx xx)
denotes the conditional distribution of the initial state given state x. Taking the log and the gradient yields the identity:
Vx log gr (x) vx (xgg:(x))((xx///)()))))))))
where 9(x,t) = Vx log Ex "
[
(10)
This additional term g, often referred to the guidance, can be approximated using known quantities such as the score function of pt and the weight function w (Chung et al.] 2023 Kim et al. (2025c; Yu al. 2023), enabling sampling from approximated g via the reverse-time SDE without any further training.
Motivated by these developments, we propose new learning framework that leverages guided sample generation to construct informative training data specifically tailored for risk-averse learning. Rather than drawing training samples uniformly from p(x), we aim to generate samples that contribute to noise reduction in risk-sensitive objectives, thereby improving model robustness to rare but high-loss events.
3.2 Risk-Averse Learning via Conditional Valuc-at-Risk
Our ultimate goal is training of risk-averse task models, in which the objective is not merely to optimize expected model performance, but to mitigate the impact of potentially rare but high-loss outcomes. We consider CVaR, one of the most widely adopted risk measures, which builds upon the concept of Value-at faltee-at-Risk -isk (VaR).
Let 0 E d denote the parameters of the task model, and let ((0; x) be the loss incurred input For a given quantile (confidence) level 8 E (0. 1), the VaR is defined as the smallest threshold a such that the loss does not exceed a with probability least 3:
VaR (0) minfa R P(E(O: XP) S af 2 (3)
where P[((O; XP) S a] = Se(e:x) p(x) dx, and the distribution is assumed to be continuous with respect to a. While VaR captures a quantile of the loss distribution, it does not reflect the magnitude of losses beyond the threshold. The Conditional Value-at-Riss addresses this by computing the expected loss in the tail beyond (0):
c0) = Ix
((0: 2 VaR
(3)
Our objective is to find model parameters H that minimize the CVaR at a given quantile level B::
argmin +
RER

---

Algorithm Risk-Averse Model Training via Loss-Guided Importance Sample Generation
Input: Initial model Bu. generative model V log Pr (x), confidence level function yp, dataset B
Output: Risk-averse model 0
1: Generate importance samples {x, [=1 q(x) x (p((O0; x)) p(x)
Bg
2: Compute Z = (xx==pls(((00: X²)]]
3: Initialize 0g
4: for k = 1 to K + do
5: Sample data pair (x, {(0o; from
q
6: MC estimation of a + Exa-g Ze0 1:x -o 1) xl
7: (0x, ax) + SuboradieetDDsscont/
0k-1,
This objective is known be equivalent to the following unconstrained optimization problem RRockfelllar and Uryasev 2000) as
0" o argmin o) where o) a Ex ((()))( a)*}.
(5)
Here, (z)* = max(x; 0) denotes the positive part function. The solution a corresponds to VaR,, and 6* minimizes CVaRg.
4 Risk-Avers Model Training via Loss-Guided Importance Samples
While the CVaR objective in (5) provides principled framework for addressing tail-risk scenarios in downstream tasks, its empirical estimation is particularly challenging, especially at high confidence levels (3 - 1). In this regime, the corresponding VaR threshold becomes large, and the expectation term Ex*~pI(E(0)) X²) a becomes increasingly difficult to estimate due to the rarity of high-loss evaluates
instances, for which (e(0; XP) a++ is nonzero. For most samples from p(x). this to zero, leading to high variance and poor gradient signals during training. Consequently, naive sampling from the base distribution p(x), even with a generative model, becomes inefficient and often requires an infeasibly large number of samples to stably estimate the CVaR objective for training.
Key Idea. To address these, propose leveraging the generative model sample from an importance-weighted distribution q(x) tailored to highlight high-loss regions. Based on the avail- ability of pretrained model On and score-based generative model capable of sampling from p(x), our approach consists of two components: (i) Sample inputs from a weighted distribution q(x) x ((((06; x)) p(x), where ip Rzo - R~o nondecreasing function that prioritizes high-loss examples. (ii) Use the importance samples to perform CVaR minimization via importance- weighted MC estimation.
Intuitively, this sample generation strategy concentrates on examples that are informative for CVaR optimization, those in the tail of the loss distribution. These rare, high-loss instances expose the model to critical failure modes and enable more effective risk-averse training. We refer to our approach as Risk-Averse Model training via loss- loss-guided Importance Samples (RAMIS).
4.1 Algorithm
Algorithm] I takes as input: an initial pretrained model 6.. score-based generative model capable of sampling from p(x), a target quantile level 33 E (0, 1). and a non-decreasing weighting function y used to construct the importance sampling distribution. We assume access to dataset B = (x: )
where each x; drawn i.i.d. from the base distribution p(x). This dataset may be externally provided or synthesized via the generative model.
Line We generate B, samples from the amportance-weighter distribution, qo (x()) q(x) x <p(((0;;)) pxx)), by guiding the generative model using loss values computed under 0p. In score- based generative models, this corresponds solving the following reverse-time SDE:
dx% = (f(X)) - o(1)² log ai (X())) di + (() dW (o)
(6)
5

---

The specific implementation of this guided importance sampling process may vary based on the chosen generative model guidance method and detailed in Appendix [B]
Line 2:
The expectation of the importance weight function ((((00; x)) over the base distribution
p(x) is computed Exx=ply<(((0; X²)) = Z. This normalization factor Z can be approximated
as Z [ ExEB (e(((() x)) and is utilized in subsequent optimization iterations.
Lines 4-7: At each training step, we draw a sample from g(x) along with its corresponding im- portance weight ((E(Ob; x))- The CVaR objective 04-1 Exyrng 2(8(0=-1:X)) -000----))))--1111 is es- timated via MC. which corresponds to a variational form in (5). Note that the likelihood ratio p(x)/q(x) simplifies Z/ Z)) We perform subgradient- based optimization using a subrou- tine SubGradi entDescent eueeeaddeeteeesnnnn (see Appendix A for details), updating both 0 and a in the direction that minimizes the estimated CVaR objective.
=(((0):99)(11))
Importance Sampling Mechanism. The proposed approach differs fundamentally from conven- tional importance sampling techniques, which re-evaluate model performance each iteration and dynamically adjust sampling probabilities over a fixed dataset. Such methods introduce additional per-iteration computational overhead (El Hanchi and Stephens 2020 Needell al., 2014 Zhao and
Zhang 2015).
In contrast, our framework adopts fixed importance sampling distribution constructed prior to training. We guide the generative model to directly produce samples from the target importance- weighted distribution. This eliminates the need for iterative reweighting per-batch loss evaluations. Importantly, during training (Lines 4-7 in Algorithm T. our method introduces no additional computational overhead beyond lightweight scalar reweighting of the loss term (((0;x) aa)
4.2 Theoretical Analysis
In this subsection, we present a convergence analysis of the proposed RAMIS framework and justify how loss-guided importance sampling improves risk-averse training. Specifically, we show that sampling from a reweighted distribution, which is biased toward high-loss regions under a reference model, reduces the noise of stochastic gradient descent.
Assumption 1 (Convexity, smoothness, and bounded loss). For all x E TRdd, E(0; x) are convex, continuously differentiable, 0 ((0;x) M < oc, and ((0; x) and the norm of Ve(0;x) are Li-soooth and Læ-Lipschitz, respectively. For all k E [0, K). |00 || S K.
Assumption T implies the standard convexity and smoothness of the loss function. We provide formal definition of convexity and smoothness in Appendix [A] Also, the parameterized model norm bounded. Building on the CVaR minimization analysis of Meng and Gower (2023), which relies on the stochastic model-based framework of Davis and Drusvyatskiy (2019). we have the following convergence property.
Theorem 1 (Convergence Rate). Suppose that Assumption 1 holds and over iterations k = 1,.... K 1, Algorithm 1 uses realizations Xs that are i..dd. with q. Let {orh be the iterates generated by Algorithm/ such that dh = (0g,ar) T, 66 is minimizer of Fg, and set dy
d For given
VK-A
quantile 3, we have
K
< [100, 00) 1-
E
FØ
Φk
Pz(0r)
(7)
K
2XV +1
VK +1
1=1
(XP'? p(X)) (1-py²
+1 and w* (x) (IV ((0xx) + 2L2x))² + +1) 1/2
where ((g)= = Exp=p
x(*)
Remark (Loss-dependent Optimization Noise). Theorem [ establishes an O(IvVK) con- vergence rate with stochastic noise term é(g) that depends on the initial loss x()::)). This dependence on the loss value is well-aligned with the standard results in stochastic optimiza- tion (Zhao and Zhang] 2015; Davis and Drusvyatskiy, 2019), where the stochastic noise is governed by the gradient of the loss. To understand this relationship more precisely, con- sider the case where the loss function satisfies a Polyak-L.ojasewiccz (PL) condition (Karimi) et al. 2016). That is, for some μ > 0 and all 0, 2p (E(A;; x) - E*) S VVl((0; x) where ming ((0:)). Note that the PL condition holds for several classes of neural networks
e"

---

Liu et al., 2019; Zhou and Liang 2017 Charles and Papailiopoulos 2018 Hardt and Ma Under L1 smoothness, (6: x] 2L, 1(6 x) and have
2016
2p (4(0n; x) (*) < V (0 x)|| < 2L, ( x).
(8)
This chain of inequalities implics that the high-loss samples contribute proportionately to the norm of the gradient.
Remark 2 (Noise Reduction via Importance Sampling). The term ö(g) in Theorem is minimized when the sampling distribution (xx) is chosen as g(x x w (x))(xx, which depends on the quantities, potentially impractical to compute in real-world scenarios. To circumvent this, we propose using a -enndecreas surrogate weighting function o IR20 + Ry that approximates the behavior of desired importance weights. Specifically, sampling from the distribution q(x) x (((((b;; x)) p(x) reduces the term i(q) relative to naive sampling from p(x) under the following condition:
(XP)²
(()) 2 i(4) = Elw" (XP)2) E
Elpp(((00; X*)]]
(e((( X²))
We observe empirically that simple choices of ip, such as the square-root or identity mapping, yield strong performance (Sec. [..T). In summary, the analysis establishes that loss -uided importance sampling based on the pretrained model can reduce the error of CVaR optimization. Rather than merely increasing the sample size, we leverage score-based generative models to synthesize samples from the proposed reweighted distribution, enabling efficient risk-averse training.
loss-guided
5
Experiments
Evaluation Summary. We evaluate the effectiveness of our proposed framework across both synthetic and real-world tasks. Specifically, aim to answer the following questions: (i) Can generate high-loss-inde iinduiin samples using score-based generative models by pretrained models? (ū) Do these samples improve downstream robustmess relative existing robust optimization methods? (iii) Does the approach generalize to high-stakes, real-world applications?
To this end, we conduct two sets of experiments: Sec. 5.T.
We evaluate method controlled regression task over a Gaussian mixture distribution to assess robustness under data heterogeneity and sample scarcity. Sec. 5.2 We apply our method to real-world wireless channel state information (CSI) compression task, demonstrating its potential practical utility.
Baselines and Fairness. We compare against strong risk-sensitive and robust optimization base- lines: Stochastic Subgradient Method (SSGM) for CVaR minimization (Meng and Gower, 2023). J DORO Zhai et al. 2021), -DRR (Namkoong and Duchi 2016), and standard ERM (i.e., CVaR at 0). All methods start from the same pretrained checkpoint and are trained on the same number of samples from the same generative model; RAMIS uses the identical budget but replaces standard samples with loss-guided (importance) samples. Running SSGM without importance sampling isolates the contribution of our loss-guided sampling scheme, while comparisons to DORO and x2-DRO test whether state-of-ther the-arr-rt robust objectives can mitigate tail risk absent our mechanism. ERM serves conventional average-risk baseline.
5.1 Risk-Averse Regression over Density- Heterogeneoous Gaussians
Task Overview. We consider a synthetic regression task where inputs x E RR2 are drawn from Gaussian mixture distribution with three components centered at (-0.6, 0.6). (0.6, 0.6), and (0.0, -0.6), each with standard deviation 0.06 but with unbalanced mixing weights of 0.01, 0.001, and 0.989, respectively (See leftmost subplot in Figure 2). The objective is to predict the second coordinate X(I] from the first X(o] using a quadratic regression model trained via risk minimization methods with Mean Squared Error (MSE) loss. This setup can pose significant challenge for robust learning due to the extreme imbalance: standard training on limited number of samples from p(x) yields poor performance on rare but critical components (e.g., the 0.01 0.001-weight modes), which dominate the tail risk.
To evaluate method, adopt two-phase training strategy. First, we obtain pretrained (reference) model 0 on 102 samples from p(x). Second, (2(x) z/2 to construct an
7

---

Table 1: CVaR (mean + std over 100 trials) across Quantile Levels 8 (lower is better).
RAMIS (ours)
SSGM
DORO
X²-DRO
ERM
0.99
0,0774 + 0.0602
0.5131 + 0.6211
0,4940 + 0,4168
0.6124 + 0.5954
0,4461 0.4415
0.95
0.0261 + 0.0156
0.1255 + 0.1406
0.1377 0.2146
0.1277 = 0.1012
0.1050
0.0963
0.90
0.0172
0.0080
0.0604 1 0.0604
0,0894 0.0903
0.0766 1 0.1154
0,0559 0.0481
0.80
0.0116
+ 0.0050
0.0329
+ 0.0295
0,0361 + 0.0422
0.0380 +: 0.0466
0.0301 0.0240
0.50
0.0069
0.0024
0.0137 0.0106
0.0134 0.0102
0.0137 + 0.0115
0.0131 0.0096
Groumd-truth
Trai Samples
Pretrained Model
Importance Samples
Risk-Averse Model
Rare
High-loss
0.01
0.001
Reg Regresson Cinve
Figure 2: Visualization of the process. From left right: (1) true data distribution p(x), (2) samples drawn from p(x), (3) pretrained model and its loss map, (4) samples drawn from g(x) ox ((((0ox)))p(s and (5) the final risk-averse model trained on these samples. The loss-guided sampling expands support to rare regions and enables robust optimization.
importance-wee weighted distribution q(x) x (p(E(0;; x)) pxx) and draw the same number of new samples from this distribution using the corresponding generative model. These samples are then used to train a risk-averse model. More detailed setup and results are provided Appendix Other choices of yp provided in Appendix E
Results. Figure visually illustrates our method. The leftmost panel shows the ground-trit -ruth distribution p(x). which includes two rare Gaussian components with low probabilities (0.01 and 0.001). depicted in the second panel, a limited number of samples drawn from p(x) rarely cover these low-density regions, resulting in limited exposure during training. Consequently, the pretrained model trained on these samples shows high loss in the low-density regions, as reflected in the loss map shown in the third panel-in the colormap, these tail regions appear in yellowish hues, indicating higher loss.
We exploit this loss landscape by constructing an importance-weighted distribution based on E(o; x) and guiding the generative model to sample accordingly. The fourth panel shows samples generated from this reweighted distribution. Despite using the same sample budget, these samples provide substantially better coverage of the support set, especially in the tails. The final panel shows that training on these importance samples leads to risk-averse model that performs reliably across both high-density and tail regions of the input space.
Table I reports the CVaR performance across varying quantile levels 3 for our method and baseline ap- proaches. Across all quantile levels, our framework (RAMIS) consistently achieves the lowest CVaR, demonstrating superior robustness in tail-risk regimes. The baseline methods without importance samples exhibit substantially higher risk. These results demonstrate that access high-loss-induccin importance samples generated via pretrained model guidance provides distinct ad advantage that cannot be matched by applying robust optimization techniques over uniformly sampled data.
5.1.1 Additional Analysis
To further assess the efficiency of the proposed framework, we analyze (i) the computational cost of generating importance-weightee samples and (ii) the effect of the weighting function yo, which controls the emphasis placed on high-loss regions. Detailed results and ablation studies are provided in Appendix
5.2 Risk-Averse Compression of Wireless Channel State Information
Task Overview. In wireless communication systems, Channel State Information (CSI) captures key physical-layer characteristics such as signal directionality, multipath components, and propagation strength between transmitters and receivers (Lin) 2022). Accurate CSI feedback from the transmitter to the receiver crucial for tasks like beamforming, scheduling, and adaptive modulation. However, modern CSI matrices are typically high-dimensional, necessitating efficient compression to support

---

Table 2: CSI Compression CVaR (mean + std over 10 trials), in units of 10-3 (lower better).
RAMIS (ours)
SSGM
DORO
X²-DRO
ERM
0.99
2.2604 0.0419
2.3413 0.0346
2,4987 0.0744
2,5594 = 0.0341
2.3442 0.0346
0.95
1.4759 + 0.0259
1,5260 0.0198
166663 : 0.0429
1.6655 + 0.0313
1.5273 4: 0.0198
0.90
1.1292 1 0.0189
1,1659 0.0130
1,2340 1 0.0258
1.2697 1: 0.0225
1.1670 1: 0.0126
0.80
0.7895
0.0127
0,8115 0.0069
0.8576 0.0100
0.8863 + 0.1122
0.8119 0.0067
0.50
0,3870
+ 0.0054
0,3954 = 0.0024
0.4029
= 0.0014
0.4169
= 0.0018
0,3953 + 0.0024
0.0013
0,2059
0.2061
0.0014
Typical samples
High- inducing (rare) samples
Figure 3: Visualization of generated samples. Left three columns: Typical samples with median
loss values sampled from the base distribution. Right three columns: High-loss samples generated by pretrained model loss-guided sampling, which exhibit a 6.2 x 10 reconstruction loss-rare and unseen across 8 10 samples from the base distribution. Top row: Spatial-frequency (Y/X) representation; Bottom row: Angular-delay (Y/X) representation.
bandwidth-constraiiee channel feedback (Guo et al. 2022p. To ensure reliable communication in practical deployments, especially under worst-case scenarios, risk-averse compression is essential.
In this experiment, assess the performance of the proposed method in the context of risk-averse CSI compression. We assume access to a pretrained score-based generative model trained on a CSI dataset generated by the Quadriga simulator (Jacckel et al.) 202I). where single CSI instance is 256 x 32 complex matrix, and baseline CSI compressor trained using ERM. The CSI compressor is implemented as vector-quantized autoencoder (van den Oord al.) 2017), comprising encoder, quantization bottleneck, and a decoder. Following Algorithm| we guide the pretrained generative model using the .SEE loss values of the initial compressor to generate informative, high-loss samples. These samples are then used to fine-tune the compressor using a EVaR-basee objective. Detailed specifications of the dataset, model architecture, and training parameters are provided in Appendix D
Table 2 reports the CVaR performance terms of reconstruction distortion (MSE) across various quantile levels 3. Lower distortion indicates better robustness. RAMIS consistently achieves the lowest CVaR in the high-risk regime (3 {0.9, 0.95, 0.99)), outperforming all baselines, in- cluding SSGM, DORO, x² -DRO, and ERM. As 3 decreases toward O, where CVaR approaches the expected loss, the performance gap narrows, and RAMIS converges with SSGM and ERM. This further indicates that RAMIS with importance samples does not degrade the average-cast performance, confirming its consistency. The performance gain at the high region supports that the conventional methods, which rely samples drawn from the original data distribution, insufficient for minimizing tail risk.
Results.
Figure 3 further illustrates the nature of the samples generated via metrained-loss-guiine importance sampling. The top row shows representations in the spatial-frequeee domain, while the bottom visualizes the corresponding angular-delay profiles, computed via 2D inverse FFT (IFFT) with truncation to the low-delay region for interpretability. The left three columns present typical generated samples from the base generative model, chosen the three median distortion examples by MSE.
By contrast, the right three columns show samples obtained via RAMIS, using the generative model guided by the pretrained model loss. These samples exhibit significantly higher reconstruction distortion, with the average MSE increasing by 4.7 x 10-4 and a maximum distortion exceeding 6 x 10-3 Notably, the corresponding angular-delay representations reveal more complex scattering patterns, indicating that the proposed framework successfully targets rare, high-loss scenarios that are otherwise underrepresented in the base distribution.

---

Discussion, Limitations of Work, and Future Directions
This paper introduces RAMIS, novel risk-averse learning framework that integrates score-based generative modeling with pretrained model feedback to synthesize high-loss, informative samples for downstream optimization. contrast to existing generative approaches that aim to increase sample diversity or generalization, our framework targets the utility of samples specifically for minimizing tail-risk objectives such as CVaR. By leveraging pretrained loss signals as importance guidance, we enable generative models to contribute directly to risk-sensitive training.
Our study primarily focuses the theoretical motivation behind loss-guided generative sampling and demonstrates its effectiveness through controlled synthetic experiments and a Nomain--spcciff application in wireless communication. While these results validate the core principles of RAMIS, broader applications remain to be explored. As diffusion-badd generative models continue to evolve and become increasingly accessible across domains where risk-sensitive optimization is critical, we expect RAMIS to generalize naturally to these settings.
Acknowledgment
This material based upon work supported by the National Science Foundation under Grant Nos. 2148224 and 2443857, the ARO Award W91 INF23 10062, and the ONR Award 0000142412543 and is supported in part by funds from OUSD R&E, NIST, and industry partners as specified the Resilient & Intelligent NextG Systems (RINGS) program and the WNCG/6G@UI @UT.
10

---

References
Mohamadreza Ahmadi, Xiaobin Xiong, and Aaron D. Ames. Risk-averse control via CVaR barrier functions: Application to bipedal robot locomotion. IEEE Control Systems Letters, 1:878-883, 2022.
Siddharth Alexander, Thomas F Coleman, and Yuying Li, Minimizing CVaR and VaR for portfolio of derivatives. Journal of Banking & Finance, 30(2):583-605, 2006.
Brian DO Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12 (3):313-326, 1982.
Fredrik Andersson, Helmut Mausser, Dan Rosen, and Stanislav Uryasev. Credit risk optimization with conditional value-at-risk criterion. Mathematical Programming. 19:273-291, 2001.
Sravan Kumar Ankireddy, Heasung Kim, and Hyeji Kim. Residual diffusion models for variable-rate joint source channel coding of MIMO CSL arXiv preprint arXiv:2505.2100 21681, 2025.
Behnaz Bahmei, Elina Birmingham, and Siamak Arzanpour. CNN-RNN and data augmentation using deep convolutional generative adversarial network for environmental sound classification. JEEE Signal Processing Letters, 29:682 686, 2022.
O Bardou, N Frikha, and G Pagès, Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling. Monte Carlo Methods and Applications, 17(3):17--100, 2009.
Qiuyu Cai, Chao Dong, and Kai Niu. Attention model for massive MIMO CSI compression feedback and recovery. In IEEE Wireless Communications and Networking Conference, pages 1-5. IEEE, 2019.
Timothy CY Chan, Houra Mahmoudzadeh, and Thomas G Purdie. A robust-CVaR optimization approach with application breast cancer therapy. European Journal of Operational Research, 238(():876-885, 2014.
Zachary Charles and Dimitris Papailiopoulos. Stability and generalization of learning algorithms that converge global optima. In International Conference on Machine Learning, pages 745-754, PMLR, 2018.
Sapana Chaudhary, Ujwal Dinesha, Dileep Kalathil, and Srinivas Shakkottai. Risk-averse fine-tuning of large language models. Advances in Neural Information Processing Systems, 37:107003 107038, 2024.
Yunhao Chen, Zihui Yan, and Yunjic Zhu. A comprehensive survey for generative data augmentation. Neuro- computing, 600:1281677 2024.
Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. ILVR: Conditioning method for denoising diffusion prohabilistic models. In IEEF/CVF International Conference Computer Vision, pages 14347-14356, 2021.
Yinlam Chow and Mohammad Ghavamzadeh. Algorithms for CVaR optimization in MDPs. Advances in Neural Information Processing Systems, 27, 2014.
Hyungjin Chung, Jeongsol Kim, Michael Thompson McCann, Mare Louis Klasky, and Jong Chul Ye. Dif- fusion posterior sampling for general noisy inverse problems. In International Conference on Learning Representations, 2023.
Erik Dahlman, Stefan Parkvall, and Johan Skold. 4G: LTE/LTE--dvaanee for mobile broadband. Academic Press, 2013.
Abdelaati Daouia, Irène Gijbels, and Gilles Stupfler. Extremiles: A new perspective asymmetric least squares. Journal of the American Statistical Association, 114(527):1366-13811 2019.
Abdelaati Daouia, Irene Gijbels, and Gilles Stupfler. Extremile regression. Journal of the American Statistical Association, 1579-199 2022.
Damek Davis and Dmitriy Drusvyatskiy. Stochastic model-based minimization of weakly convex functions. SIAM Journal on Optimization, 29(1)-207-239 2019.
Anand Deo and Karthyek Murthy. Efficient black-box importance sampling for var and CVaR estimation. In 2021 Winter Simulation Conference (WSC), pages 1- 12. IEEE, 2021.
Ayoub El Hanchi and David Stephens. Adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Advances in Neural Information Processing Systems, 57702-177773 2020.
Carlo Filippi. Gianfranco Guastaroba, and Maria Grazia Speranza. Conditional value-at-ris at-risk beyond finance: a survey. International Transactions in Operational Research, 27(3):1277-1399 2020.
11

---

Jiajaa Guo, Chao-Kai Wen, Shi Jin, and Geoffrey Ye Li. Overview of deep bearning-based CSI feedback in massive MIMO systems. IEEE Transactions Communications, 70112):801780045, 2022.
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. arXiv preprint arXiv: 2016.
Shengyi He, Guangxin Jiang. Henry Lam, and Michael C Fu. Adaptive importance sampling for efficient stochastic root finding and quantile estimation. Operations Research, 72(6):6122-2600, 2024a.
Tianyu He, Peiyi Han, Shaoming Duan, Zirui Wang, Wentai Wu, Chuanyi Liu, and Jianrun Han. Generative data augmentation with differential privacy for non-IlI problem in decentralized clinical machine learning. Future Generation Computer Systems, (60:171-18: 2024b.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion prohabilissic models, In Advances in Neural Information Processing Systems, pages 6840-6851, 2020.
Stephan Jaeckel, Leszek Raschkowski, Kai Börner, and Lars Thiele. QuaDRiGa: 3-D multi-cell channel model with time evolution for enabling virtual field trials. IEEE Transactions on Antennas and Propagation, 62(6):3242 225566222266, 2014.
Stephan Jacckel, L Raschkowski, Börner, L Thiele, Burkhardt, and E Eberlein. QuaDRiGa-quasi determin- istic radio channel generator, user manual and documentation, 2021.
Hamed Karimi, Julie Nutini, and Mark Schmidt. Linear convergence of gradient and proximal-gradee methods under the polyak-lojasiewicz condition. In Joint European conference on machine learning and knowledge discovery in databuses. pages 195-811. Springer, 2016.
Heasung Kim, Tackyun Lee, Hyeji Kim, and Gustavo Veciana. Importance sampling via score-based generative models. arXiv preprint arXiv:2502.044:: 2025a.
Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo De Veciana, Mohamed Amine Arfaoui, Asil Koc, Phil Pietraski, Guodong Zhang, and John Kaewell. Generative diffusion model-based compression of MIMO CSL In ICC 2025 IEEE International Conference on Communications, pages 6323 6328, 2025b.
Sunwoo Kim, Minkyu Kim, and Dongmin Park. Test-time alignment of diffusion models without reward over-optimization. In The Thirteenth International Conference on Learning Representations, 2025c.
Tackyun Lee, Juseong Park, Hyeji Kim, and Jeffrey G Andrews. Generating high dimensional user-specific wireless channels using diffusion models. IEEE Transactions on Wireless Communications. 2025.
Xingqin Lin. overview of 5G advanced evolution in 3GPP Release 18. IEEE Communications Standards Magazine, 6(3):77-83 83, 2022.
Mingrui Liu, Zhuoning Yuan, Yiming Ying, and Tianbao Yang. Stochastic AUC maximization with deep neural networks. arXiv preprint urXiv:190S: 10831, 2019.
Yusha Liu and Osvaldo Simeone. Hypermn: Deep learning-aide downlink CSI acquisition via partial channel reciprocity for FDD massive MIMO. In IEEE International Workshop on Signal Processing Advances in Wireless Communications, pages 31 35-3. IEFE, 2021.
Zhilin Lu, Jintao Wang, and Jian Song. Multi-resolution CSI feedback with deep learning in massive MIMO system. In IEEE International Conference on Communications, pages 1-6. IEEE, 2020.
Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher Yu, Radu Timofte, and Luc Van Gool. Repaint: Inpainting using denoising diffusion probabilistic models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11461-18 11471, 2022.
Si Yi Meng and Robert M Gower. A model-based method for minimizing CVaR and beyond. In International Conference on Machine Learning, pages 24436-24456. PMLR, 2023.
Hongseok Namkoong and John C Duchi. Stochastic gradient methods for distributionally robust optimization with f-divergences. In Advances in Neural Information Processing Systems, 2016.
Dcanna Needell, Nathan Srebro, and Rachel Ward. Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. In Advances in Neural Information Processing Systems, 2014.
Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, pages 8162-8171. PMLR, 2021.
R Tymell Rockafellar and Stanislay Uryasev. Optimization of Conditional Value-at-Rin Risk. Journal of risk, 2: 21 12-42,22 2000.
12

---

Siyu Shao, Pu Wang, and Rugiang Yan. Generative adversarial networks for data augmentation in machine fault diagnosis. Computers in Industry, 106:85-93, 2019.
Shivashankar and Shane Miller. Semantic data augmentation with generative models. In Proceedigss of the JEEE/CVF Conference on Computer Vixion and Puttern Recognition, pages 863-873, 2023.
Tasuku Soma and Yuichi Yoshida. Statistical learning with conditional value risk. arXiv preprint arXiv:2002.0582 2020.
Yang Song. Jascha Sohl-Dickste Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021.
Aviv Tamar, Yonatan Glassner, and Shie Mannor. Optimizing the CVaR via sampling. Proceedings of the AAAI Conference on Artificial Intelligence, 2015.
Zhongfu Tan, Guan Wang. Liwei Ju. Qingkun Tan, and Wenhai Yang. Application of CVaR risk aversion approach in the dynamical scheduling optimization model for virtual power plant connected with wind- photovoltaic- storage system with uncertainties and demand response. Energy, 124:198- 213,, 2017.
Brandon Trabucco, Kyle Doherty, Max Gurinas, and Ruslan Salakhutdinov. Effective data augmentation with diffusion models. arXiv preprint arXiv: 2023.
Dylan Troop, Frédéric Godin, and Jia Yuan Yu. Bias-corrected telks-over-threshol estimation of the CVaR. In Uncertainty in Artificial Intelligence, pages 1809-1818. PMLR, 2021.
Aaron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural discrete representation learning. In Advances in Neural Information Processing Systems, 2017.
Patrick von Platen. Suraj Patil, Anton Lozhkov, Pedro Cuenca, Nathan Lambert, Kashif Rasul, Mishig Davaadorj. Dhruv Nair, Sayak Paul, William Berman, Yiyi Xu, Steven Liu, and Thomas Wolf. Diffusers: State-of-the-art diffusion models. /estps//ggitae
com/ wwo.//hggiggfaaae www.ae/ggacaeeoooooo www.c///ddfffrffreeeeeee 2022.
Tianqi Wang. Chao-Kai Wen, Shi Jin, and Geoffrey Ye Li. Deep learning- based CSI feedback approach for tare-varying massive MIMO channels. IEEE Wireless Communications Letters, 8(2):416-419, 2018.
Yinong Oliver Wang, Younjoon Chung, Chen Henry Wu, and Fernando De la Torre. Domain gap embeddings for generative datasct augmentation. In Proceedings of the IEEE/CVP Conference Computer Vision and Puttern Recognition (CVPR), pages 28684-28694, 2024a.
Zaitian Wang, Pengfei Wang, Kunpeng Liu, Pengyang Wang, Yanjie Fu, Chang- Tien Lu, Charu C Aggarwal, Jian Pei, and Yuanchun Zhou A comprehensive survey on data augmentation. arXiv preprint 1:X.v:2405.0959 2024b.
Chao-Kai Wen, Wan-Ting Shih, and Shi Jin. Deep learning for massive MIMO CST feedback. IEFE Wireless Communications Letters, 7(5):748-751, 2018.
Linna Xu and Yongli Zhu, Generative modeling and data augmentation for power system production simulation. In NeurIPS 2024 Workshop Data-driven and Differentiable Simulations, Surrogates, and Solvers, 2024.
Wei Yang. Chi Lin, Haipeng Dai, Pengfei Wang, Jiankang Ren, Lei Wang, Guowei Wu, Qiang Zhang. Robust wireless rechargeable sensor networks. JEEE/ACM Transactions on Networking, 31(3):949-966 2022.
Jiwen Yu, Yinhuai Wang, Chen Zhao, Bernard Ghanem, and Jian Zhang. Freedom: Training-free energy-guided conditional diffusion model. Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 24184424444.111 2023.
Ali Zaidi, Fredrik Athley, Jonas Medbo, Ulf Gustavsson, Giuseppe Durisi, and Xiaoming Chen. 5G Physical Layer: principles, models and technology components. Academic Press, 2018
Runtian Zhai, Chen Dan, Zico Kolter, and Pradeep Ravikumar. DORO: Distributional and outlier robust optimization. In International Conference on Machine Learning, pages 12345-12355. PMLR, 2021.
Peilin Zhao and Tong Zhang. Stochastic optimization with importance sampling for regularized loss minimization. In International Conference on Machine Learning, pages 1-9. PMLR, 2015.
Chenyu Zheng, Guoqiang Wu, and Chongxuan Li. Toward understanding generative data augmentation. In Advances in Neurul Information Processing Systems, pages 54046-54064 2023.
Yi Zhou and Yinghin Liang. Characterization of gradient dominance and regularity conditions for neural networks. arXiv preprint arXiv:1710.069100 2017.
13

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The abstract and introduction accurately reflect the paper's contributions and scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
Limitations are discussed in Section 6.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
14

---

Justification:
It provides the full set of assumptions and a complete and correct proof.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless whether the code and data are provided or not)?
Answer: [Yes]
Justification: Yes, the implementation details provided along with source code.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how to reproduce that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architccture clearly and fully.
(c) If the contribution is new model (e.g., a large language model), then there should either way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reprodueibility. the case of closed-source models, may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
15

---

Answer: [Yes]
Justification:
Yes, we provide Github link.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips... cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https Coooeoooddesssseeeeee 7/ cttppsscccpbbbccpppecccccc / ssiniiiicyy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Does the paper specify all the training and test details (c.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Question:
Answer: [Yes]
Justification:
The paper specifies all the implementation details in the appendices.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, appendix, as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: Yes. We provide the standard deviation of the performance under multiple random seeds.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the enror bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
16

---

It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: Yes. This work provides sufficient information regarding the computational resources for the experiments.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (c.g., preliminary or failed experiments that didn't 't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics http:///wwaupp.ccpppp..//ataaaaa
Answer: [Yes]
Justification: Yes. This work complies with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: There is no specific societal impact of the work.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
17

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of MI..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
This paper does not pose such risks.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Lieenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: Yes. All external assets properly credited.
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
18

---

If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: Yes. The implementation code is clearly documented and released with the paper.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Question:
Answer: [NA]
Justification:
This paper does not involve crowdsourcing research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [NA]
Justification: This paper does involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, not include any information that would break anonymity (if applicable), such the institution conducting the review.
19

---

16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, originality of the research, declaration is not required.
Answer: [NA]
Justification: The main method development in this research does not involve LLMs.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to L.LM policy hattaa///aaarrpssscc///offeeeere for what should or should not be described.
20


Reviews:
[{"review_id": "pkFNr3CiMh", "reviewer": "Reviewer_hgR6", "summary": "The paper provides a new approach for optimizing conditional value-at-risk (CVaR) over distributions generated from diffusion-based generative models. The primary challenge of optimizing CVaR is typically due to being able to efficiently sample high loss samples in order to reduce the variability of CVaR objective. To address the challenge, the paper's approach proposes an algorithm for reweighting the sampling distribution of the generative diffusion models and theoretically analyze the convergence of their approach. They conclude with numerical experiments that compare their approach with benchmark approaches on the same sampling budget and show their approach better optimizes CVaR.", "questions": "1. Can any comparison be made about the theoretical convergence rate between the proposed method and other benchmark methods? For example, how does the rate presented in this paper compare to the rates SGM, DORO, etc.? Similarly, how does the analysis differ from previous works that also use importance sampling for non-generative models?\n\n2. It's not clear to me how to select $\\phi$, are there empirical results that compare different choices of $\\phi$?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The paper provides a straightforward and effective method for improving the efficiency of generating accurate estimates of CVaR. The approach highlighted by Algorithm 1 and corresponding descriptions for each line were clear and easy to follow. \n2. The paper's theoretical analysis seems correct and provides good motivation for why their approach is effective and what inputs affect the convergence rate. The provide remarks are useful in highlighting challenges in their approach and heuristic solutions for addressing the challenges. \n3. The work feels relevant and important given recent works in generative models. Given the complexity of such models and their outputs, it makes sense that obtaining sufficient samples to optimize metrics like CVaR would be costly. Moreover, given the prevalance of these models, it makes sense that practitioners would be interested in training models that optimize the CVaR of outcomes that leverage these models. \n4. The numerical section while simple highlights intuition for why the proposed approach is effective. Leveraging real-world data also highlights the practical effectiveness of their method.\n\nWeaknesses\n1. The paper does not compare or comment on their theoretical analysis with past work so it's hard to fully understand the significance of their analysis. For example, is the theoretical result similar to past works that work with a fixed dataset or monte-carlo simulation. Similarly, it's unclear if the other methods used in the numerical section achieve similar rates or how it could be substantively different. \n2. The numerics section's synthetic experiment provides limited evaluation as the authors could also include results that study the convergence rate of their approach compared to benchmarks. They could also compare different choices of $\\phi$.", "was_revised": true, "final_justification": "After reviewing the author's rebuttal which cleared up my remaining questions and the reviews of other reviews, I will maintain my score of 5. While the numerics may be limited, the approach seems straightforward and effective which warrants an acceptance.", "rebuttal": "We thank the reviewer for the constructive and thoughtful feedback. For clarity, we have merged related points from the review into grouped responses below.\n\n[**R1Q1**] Convergence rate. The paper does not compare or comment on their theoretical analysis with past work... /  Can any comparison be made about the theoretical convergence rate between the proposed method and other benchmark methods? ... rate presented in this paper compared to the rates SGM, DORO, etc.?  / How does the analysis differ from previous works?\n\n[**R1A1**] \nThank you for the valuable comment. Under Assumption 1, our method achieves an $\\mathcal{O}(1/\\sqrt{K})$ convergence rate in iteration complexity, as shown in Theorem 1. This rate is consistent with the rate for the baseline objectives, though derived under distinct assumptions as part of them having distinct objective function. For instance, DORO  [Zhai et al., 2021] achieves the same rate under the assumption that the corresponding objective (line 991) satisfies the same standard convexity and Lipschitz continuity (Assumption 1) and $\\chi^2$-DRO can rely on a finite f-divergence constraint and employ mirror descent [Namkoong & Duchi, 2016], achieving the same rate. Optimization with the ERM objective also achieves $\\mathcal{O}(1/\\sqrt{K})$ without any changes in assumptions.  SGM is the fair baseline, as it has the same CVaR objective. Notably, our method reduces to SGM when the importance weight $w^*$ is a constant (cf. Eq. (7)), yielding the same convergence rate $\\mathcal{O}(1/\\sqrt{K})$. This equivalence is expected, typically, importance sampling does not improve the asymptotic convergence rate, but rather the constant factor via noise reduction [Zhao & Zhang, 2015].\n\nThe key theoretical distinction of our work lies in reducing the stochastic noise floor via pretrained loss-guided sampling: \nWe provide a bound on the stochastic noise term $\\hat{v}(q)$, which is minimized when sampling from $q(x)\\propto w^* (x)p(x)$ where $w^*(x)=(\\sqrt{ 2L_{1}\\ell(\\theta_0;x)}+2L_{2} \\kappa)^2 + 1$. Note that this analysis differs from previous works that use importance sampling, as we explicitly connect the importance sampling weight function to the loss value of the given pretrained model. This analysis enables a practical design of $\\varphi(\\ell)$, and under Assumption (9), the pretrained-loss guided sampling distribution achieves a tighter upper bound on the stochastic noise compared to standard sampling (e.g., SGM). \n\nNone of the existing baselines in CVaR optimization or importance sampling provides a stochastic-noise-sensitive analysis that incorporates pretrained models into the sampling distribution.\n\nWe will add this discussion and the distinct theoretical contribution in the revised manuscript.\n\n\n---\n\n[**R1Q2**]  Empirical results that compare different choices of $\\varphi$? / How to choose $\\varphi$? \n\n[**R1A2**] We thank the reviewer for raising this important question.\n\nThe desired form of  $\\varphi$ is derived in Eq (7) and given by $\\varphi(\\ell)=(\\sqrt{\\ell}+\\frac{2L_{2}\\kappa}{\\sqrt{2L_{1}}})^2 + 1/(2L_1)$ as stated in the Appendix (line 1116). This form arises from matching the optimal importance sampling distribution that minimizes the stochastic noise $\\hat{v}(q)$ in Thm 1.\n\nHowever, in practice, the exact constants $L_{1}, L_{2}$ and $\\kappa$ are typically unknown or difficult to estimate. To address this, we propose a practical surrogate $\\varphi(\\ell) = \\ell + c$ where $c$ is a tunable constant. This approximation preserves the dominant order of the loss and offers a simple yet effective implementation.\n\nTo empirically study the effect of different $\\varphi$, we conducted ablations in Appendix, Section E.2 (Impact of Importance Level Emphasis). We varied $c\\in \\{0.001, 0.01, 0.1, 1, 10\\}$ and evaluated performance across a range of $\\beta$ values (quantile). The results show that the method is robust to the choice of $c$, especially at high $\\beta$, (e.g., for $\\beta=0.99$ the proposed method consistently outperforms all the baselines with all $c$. For $\\beta=0.5$, $c\\in \\{0.001, 0.01, 0.1\\}$ lead to performance improvement). It indicates that when large-loss-inducing samples are strongly emphasized, the precise tuning of $\\varphi$ becomes less critical.\n\nWe agree that this analysis is important and will add this discussion to the main paper in the revised submission for clarity.\n\n---\nWe thank the reviewer again for the valuable feedback. We believe the revised discussion addresses the concern, and we respectfully ask the reviewer to consider increasing their score. We would be happy to provide further clarification if helpful.\n\n\n[Ref-R1-1] Zhao, Peilin, and Tong Zhang. \"Stochastic optimization with importance sampling for regularized loss minimization.\" _International Conference on machine learning_. PMLR, 2015."}, {"review_id": "48fWoOLEKv", "reviewer": "Reviewer_dRNj", "summary": "This paper develops an interesting approach to using guided generative models to produce synthetic data samples for more robust optimization of the conditional value-at-risk (CVaR). Training for good CVaR is challenging, especially when the target risk quantile is quite high. At these extreme quantiles the events that we would like to produce low-loss predictions for are very rare, and therefore relying on standard datasets to measure and optimize empirical estimates of the CVaR leads to very high variance. This work leverages generative models with guidance to (1) sample from a distribution $q(x)$ that is tilted towards high-loss samples, i.e., $q(x) \\propto \\phi(\\ell(\\theta_0; x))p(x)$, and then (2) use importance weighting on samples from $q$ to minimize a MC estimate of the CVaR. The idea takes advantage of existing ideas in generative modeling and importance weighted optimization, but is elegantly designed and well-motivated.", "questions": "- I'm curious about the effect that the method has on the standard risk. In Table 2 we start to see ERM improve over RAMIS for lower values of $\\beta$. While its expected that methods that optimize the CVaR will not also optimize the standard empirical risk, it would be nice to show these results in the table as well --- even if just to understand the tradeoffs.\n\n- I understand that the fixed importance sampling distribution is computationally efficient, but am curious about how sensitive this is to the choice of the initial model $\\theta_0$. For example, if $\\theta_0$ is uniformly bad, it will not be informative. Is there any other reason _not_ to iterative update the reference model used for loss guidance?\n\nMinor comments:\n- L256 / L291 / Table 1 acronym confusion: Do you use the stochastic subgradient method, the stochastic prox-linear method, or the SPL+ method of the cited Meng & Gower? (And if the latter, please specify a different acronym that SGM, as SGM is already widely used in the paper).", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "As described above, I think that the main idea in the paper makes sense, is well described, and forms a nice connection between recent advances in generative modeling with guidance and data augmentation techniques for risk-averse optimization. The convergence analysis and the connection to importance weighting reducing the variance of the stochastic gradient update provide further support and justification for this approach (which are aligned with standard results in the literature). That said, the empirical results are a bit weak (as I believe the authors already somewhat acknowledged in their discussion of limitations and future directions). Specifically, the paper evaluates on one synthetic task and just one real data task on wireless communications. It would be more compelling to see results on tasks where generating high quality samples may be more challenging --- such as in image generation or text sequences (e.g., to name a few suggestions: optimizing CVaR for image classification in ImageNet, radiology report generation on MIMIC-CXR, or reward modeling / preference learning on language model responses).", "was_revised": true, "final_justification": "I do believe the contribution is good and well presented as written above. Still, the evaluation is limited as the authors have acknowledged.", "rebuttal": "**[R2Q1]** -   ...the effect that the method has on the standard risk. In Table 2 we start to see ERM improve over RAMIS for lower values of $\\beta$. While its expected that methods that optimize the CVaR will not also optimize the standard empirical risk, it would be nice to show these results in the table as well --- even if just to understand the tradeoffs.\n\n**[R2A1]** We thank the reviewer for the insightful comment.\n\nIn Table 2, each row corresponds to a different value of $\\beta$. As $\\beta$ decreases, the CVaR objective gradually approaches the standard ERM. In fact, when $\\beta = 0$, CVaR becomes equivalent to ERM, and RAMIS can be directly used for minimizing the standard empirical risk. To fully address the reviewer’s suggestion, we conduct two complementary analyses.\n\n**(1) Standard ERM performance with $\\beta = 0$:**\nFirst, based on the same configuration corresponding to Table 2, we set $\\beta = 0$ for the objective and all methods under the standard ERM. Below table shows the results (in unit of $10^{-3}$).\n|   | RAMIS (ours)     | SGM             | DORO             | χ²-DRO           | ERM              |\n|-------|------------------|------------------|------------------|------------------|------------------|\n| $\\beta=0$  | 0.2032  | 0.2032  | 0.2029  | 0.2029   | 0.2028  |\n\nIn this case, the CVaR objective function is equivalent to ERM. As they are minimizing the same objective function, their performance is nearly identical, as expected.\n\n(2) Evaluating trained models at different non-target quantile levels:\n\nNext, we fix $\\beta = 0.99$ (1% tail-risk focus) and evaluate the resulting models **across a range of quantile levels** $\\beta$\n| β     | RAMIS  | SGM             | DORO             | χ²-DRO           | ERM              |\n|-------|------------------|------------------|------------------|------------------|------------------|\n| 0.99 (true target) | **2.10 ± 0.0028**    | 2.21 ± 0.0341    | 2.28 ± 0.0032    | 2.50 ± 0.2330    | 2.22 ± 0.0016    |\n| 0.95  | **1.41 ± 0.0283**    | 1.43 ± 0.0153  | 1.49 ± 0.0034  | 1.72 ± 0.2293  | 1.44 ± 0.0019  |\n| 0.90  | **1.09 ± 0.0121**    | 1.10 ± 0.0059  | 1.14 ± 0.0029  | 1.38 ± 0.2267  | 1.10 ± 0.0018  |\n| 0.80  | 0.77 ± 0.0028    | 0.78 ± 0.0012  | 0.80 ± 0.0014  | 1.02 ± 0.2249  | **0.76 ± 0.0013**  |\n| 0.50  | 0.39 ± 0.0069    | 0.41 ± 0.0038  | 0.43 ± 0.0004  | 0.63 ± 0.2251  | **0.38 ± 0.0003**  |\n| 0.00  | 0.21 ± 0.0048    | 0.23 ± 0.0045  | 0.24 ± 0.0005  | 0.44 ± 0.2229  | **0.20 ± 0.0001**  |\n\nThese results highlight the expected tradeoff: RAMIS, the proposed method, achieves superior performance in target high-risk regimes (target $\\beta=0.99$ and $\\beta=0.95, \\beta=0.9$), while ERM excels in average-case scenarios. This supports the intuition that optimizing for CVaR enhances robustness to rare, high-loss inducing samples, at the potential cost of standard performance.\n\nWe will include these results and discussions in the revised manuscript. We thank the reviewer again for raising this important point.\n\n---\n**[R2Q2]** - The empirical results are a bit weak (as I believe the authors already somewhat acknowledged in their discussion of limitations and future directions)...\n\n**[R2A2]** Our synthetic experiment was intentionally designed as a controlled setting to rigorously evaluate the core mechanism of RAMIS, whether our framework can identify and generate high-loss inducing samples that are often missed by standard sampling, by using a pretrained initial model. By constructing a Gaussian mixture with extreme mode imbalance (Fig. 2), we create a challenging yet interpretable testbed to directly visualize sample coverage and assess risk sensitivity.\n\nWe evaluate RAMIS on wireless CSI compression to demonstrate its applicability to high-dimensional, practical data where compression robustness to rare but high-distortion channel conditions is essential. This task exemplifies a real-world setting where standard training underrepresents such cases, and improved risk sensitivity directly translates to better signal reconstruction under challenging conditions.\n\nThat said, we agree that applying RAMIS to broader domains is an important next step, and we plan to explore such extensions in future work.\n\n---\n**[R2Q3]** -   I understand that the fixed importance sampling distribution is computationally efficient, but am curious about how sensitive this is to the choice of the initial model. For example, if is uniformly bad, it will not be informative. Is there any other reason not to iterative update the reference model used for loss guidance?\n\n**[R2A3]**   Thank you for this question. \n\n[Fixed Importance Sampling Distribution] As the reviewer noted, a primary motivation for using a fixed importance sampling distribution is **computational efficiency**: it avoids repeated loss evaluations, recomputation of the normalization constant, and allows reuse of generated samples. Iteratively updating the sampling distribution per optimization step introduces significant overhead, as highlighted in prior literature (e.g., Zhao & Zhang, 2015). Rather than performing per-step updates, our practical importance sampling distribution design focuses on minimizing the stochastic noise bound, i.e., the final expected model gap.\n\n[Choice of $\\theta_0$]\nMoreover, our framework is designed for the **fine-tuning** setting, assuming access to a reasonably informative pretrained model $\\theta_0$, as reflected in the title of this work. Pretrained models for many tasks are now widely available and can serve as strong baselines and provide informative guidance for importance sampling. In typical fine-tuning scenarios, only a small number of additional training iterations are required compared to training from scratch. Empirically, we demonstrate that using a fixed importance sampling distribution in this regime yields superior performance compared to existing robust optimization baselines.\n\n If a pretrained model $\\theta_0$ assigns uniformly low or high losses, it indicates the absence of a meaningful loss tail—i.e., a scenario where risk-sensitive training is unnecessary. \n \nUsing an untrained or randomly initialized model (e.g., $\\theta_0 = 0$) leads to uninformative importance weights, since the loss-induced distribution fails to highlight relevant failure modes. *Such scenarios are outside the scope of our intended use case*, which targets the increasingly common setting where pretrained models are available and serve as reasonable reference surrogates.\n\n[Iterative Application] \nThat said, **RAMIS is fully compatible with iterative refinement**. Specifically, Algorithm 1 can be applied recursively: the model $\\theta_K$ obtained from one round can serve as the new reference model for generating the next round of guided samples. Our theoretical analysis remains valid under this substitution, and the bound in Eq. (7) becomes strictly tighter due to improved reference model quality.\n\nIn our experiments, the fixed pretrained-model loss guided importance sampling distributions already achieve strong CVaR performance. However, when starting from an untrained model that requires many iterations to converge, repeated application of RAMIS will lead to improved performance. \n\n\nWe will clarify these points in the final version of the manuscript and explicitly state that RAMIS supports iterative application when appropriate.\n\n\n[Ref-R2-1] Zhao, Peilin, and Tong Zhang. \"Stochastic optimization with importance sampling for regularized loss minimization.\" _International Conference on machine learning_. PMLR, 2015.\n\n---\n**[R2Q4]**-   L256 / L291 / Table 1 acronym confusion\n\n**[R2A4]** Thank you for the careful proofreading. In L256 and Table 1, \"SGM\" refers to the Stochastic Subgradient Method, where SPL is a typo, which should be SGM. We will revise the manuscript to remove redundant or conflicting abbreviations.\n\n\n---\nWe appreciate the reviewer’s valuable feedback again. We believe the revised discussion addresses all the concerns, and we kindly ask the reviewer to consider a higher score. We are happy to provide additional clarification if needed."}, {"review_id": "HnKif6EWqq", "reviewer": "Reviewer_uMpj", "summary": "The paper proposes to use generative models to sample high risk samples for efficient distributionally robust learning. The authors design an appropriate algorithm that takes advantage of guided generative models to do some form of \"online importance sampling\". The authors present convergence guarantees of their approach. They illustrate the relevance of their approach on synthetic and real datasets.", "questions": "- See first weakness point. Can the authors explain why the samples are guided using only the initial point? Why aren't samples refined with new predictors? Please consider reading some of the references given in that part. I sincerely believe that there was a slight misunderstanding on what distribution really matters, but please correct me if I'm wrong. Maybe what the authors missed to highlight is that their procedure should only be used after a first round of empirical risk minimization? \n- Can the authors prove the reduced variance they hope their method can bring (on both losses and subgradients)?\n- Can the authors explain how they chose the other methods they compared to?\n- Can the authors try experiments using extremile rather than the CVAR?", "limitations": "See weakness part.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strengths**:\n- The idea is original, interesting, and can open fruitful avenues both in theory and in practice.\n- The empirical illustrations are well crafted. \n\n**Weaknesses**:\n- The distribution of the losses depends not only on the inputs but also on the predictor. So generating adverse samples from the distribution of the losses at the initial point, does not necessarily reflect the adequate tail distribution of the losses at the predictor we want to use. Consider taking $\\theta_0 = 0$, would the corresponding guided samples be relevant? Probably not. If $\\theta_0$ was the optimum of the ERM, then the guided samples would probably be relevant but this highlights the problem: the distribution of losses one wants the tails of depend on the predictor. Said differently, distributionally robust learning is fundamentally a min-max problem, i.e., best predictor over worst possible distribution around training distribution. What the authors have is essentially a single \"max\" step i.e., a single step towards getting a \"hard\" distribution from the initial point, but this should be iterated. An effective algorithm would probably consist in iterating the current proposal several times. Weirdly the authors argue in favor of this \"fixed importance sampling distribution\", which I don't understand. An ideal way to frame the contribution will probably to fully write the original problem in terms of distributions, see Preliminaries in [1] for example. \n- The key part of the algorithm (and where it changes from usual distributionally robust optimization (DRO)) is in having access to low variance unbiased estimates of the loss and the subgradients of the CVAR objective in $\\alpha$, $\\theta$ (so the MC step in the algorithm). The authors do not show that key point. Their argument goes through proving the convergence of the algorithm by some means and with some bounds from which they argue what should be the choice of initial distribution. This circumvolved path hides whether the claimed objective of the authors \"getting low variance oracles for optimization\" is reached or not.\n- CVAR is not the only risk-sensitive measure that could be used. Spectral risk measures like the extremile [2] partially avoid the problem of CVARs thresholding (see also [3] for optimization of spectral risk measures). That said adequate estimation of tails are always at the core of distributionally robust learning even if some other risk measure than the CVAR is used.\n- The overall idea hinges upon the assumption that the generative model is sufficiently good to generate high risk data points when such high risk data points are not present in the data. In other words it hinges upon the generalization capabilities of the generative model. It would be best to formalize this, i.e., what generalization capabilities are assumed on the generative model for the overall approach to work. Once again formalizing the problem as in [1] could help.\n- Assumptions on Theorem 1 are rather stringent (assuming bounded loss for risk-sensitive applications is always a bit counter intuitive and having other research works making the same assumptions is not a good reason for this). That said, as long as the theoretical results are meaningful to understand (i) the relevance of the approach, (ii) how to further refine e.g. parameters, that's fine. As said above, it would be best for the results to show e.g. lower variance of the stochastic estimates.\n- Eq; 8: the bound on square gradient norms does not give a bound on the variance. So the whole argument does not seem sound.\n- While the illustrations are very well done, the choice of competing algorithms is not very well justified. Namely, the given contribution could be seen as some form of importance sampling (though not refined over iterates). It would be interesting to compare to such approaches.  For example, [1] provided for example analyses of DRO in online learning setup that would be relevant here. \n\n[1] Levy, Daniel, et al. \"Large-scale methods for distributionally robust optimization.\" Advances in Neural Information Processing Systems 33 (2020): 8847-8860.\n[2] Daouia, Abdelaati, Irene Gijbels, and Gilles Stupfler. \"Extremile regression.\" Journal of the American Statistical Association 117.539 (2022): 1579-1586.\n[3] Mehta, Ronak, et al. \"Distributionally Robust Optimization with Bias and Variance Reduction.\" The Twelfth International Conference on Learning Representations.", "was_revised": true, "final_justification": "The idea is original and can really open up fruitful avenues for both theory and practice.\nThe theoretical part is somewhat lacking but it will be a great opportunity for other researchers.\nThe authors fully addressed all my concerns in a very detailed way. With the hope that they will incorporate their answers to their final version I raised my score to acceptance.", "rebuttal": "We sincerely thank the reviewer for the thoughtful and constructive feedback. For clarity, we refer to individual points using **Q** (Questions) and **W** (Weaknesses), e.g., Q1 refers to the first bullet under _Questions_, W1 to the first under _Weaknesses_.\n\n---\n**[R3Q1]**  (Q1, W1) . Consider taking $\\theta_0 = 0$... Can the authors explain why the samples are guided using only the initial point? Why aren't samples refined with new predictors? /... Maybe what the authors missed to highlight is that their procedure should only be used after a first round of empirical risk minimization?\n\n**[R3A1]**  Thank you for raising this point. We have addressed this question in conjunction with a related question from Reviewer dRNj in **[R2Q2]** and its corresponding response **[R2A2]**. Kindly refer to **[R2A2]** for our detailed explanation.\n\n---\n\n**[R3Q2]**  (Q2, W6, W2, W5) Eq; 8: the bound on square gradient norms does not give a bound on the variance... / Can the authors prove the reduced variance they hope their method can bring (on both losses and subgradients)? /  The key part of the algorithm is in having access to low variance unbiased estimates of the loss and the subgradients of the CVAR objective ... Their argument goes through proving the convergence of the algorithm by some means and with some bounds from which they argue what should be the choice of initial distribution. This circumvolved path hides whether the claimed objective of the authors \"getting low variance oracles for optimization\" is reached or not.... / ... it would be best for the results to show e.g. lower variance of the stochastic estimates.\n\n**[R3A2]** We appreciate the reviewer’s insightful comments.\n\nFirst, we clarify that our method targets reduction of the overall stochastic noise upper bound $\\hat{v}(q)$, rather than explicitly minimizing the variance of per-iteration subgradients or per-iteration loss estimates. Our primary goal of designing importance sampling distribution is to minimize the distance between the final trained parameter and the true optimum, as stated in Theorem 1. \n\nRegarding (8), it is introduced to justify our use of an importance sampling distribution proportional to the pretrained model's _loss_. While classical variance reduction analyses for SGD often optimize sampling proportional to the gradient norm squared (Zhao & Zhang, 2015), Eq. (8) shows that the gradient norm is bounded both above and below by a linear function of the loss under the PL condition. This supports our surrogate choice of the pretrained model loss as a practical proxy for gradient magnitude. In other words, *we do not claim that we minimize the gradient squared norm's upper bound*, instead, Eq (8) shows the proportional relationship between the gradient norm and the loss value. \n\nThe reason we use the term “variance” following Eq. (8) is that, by taking expectation over the inequality, we obtain a second-order moment of the gradient norm. And the expectation of the pretrained model’s loss appears in $\\hat{v}(q)$ with the optimal importance weight function $w*$ (substitution of $w^*$ into $\\hat{v}(q)$). We agree that referring to this as “variance” is misleading, and we will revise the statement at line 230 to: _“high-loss samples contribute proportionately to the squared norm of the gradient.”_\n\nThat said, we fully agree that demonstrating subgradient variance reduction is important. To fully address the reviewer's concern, we provide additional analysis regarding the subgradient and loss. Theorem 1 and Appendix Eq. (20), inherently address this. The subgradient of the $k$-th iteration objective is denoted $g_k$, and its squared norm is bounded as:\n $\\Vert g_k \\Vert^2 \\le v(x)^2$ where  $v(x) = \\sqrt{ \\frac{1}{(1-\\beta)^2}\\Vert \\frac{p(x_k)\\partial \\ell (\\theta_k;x_k)}{q(x_k)} \\Vert^2 + 1 +\\frac{p(x_k)^2}{q(x_k)^2 (1-\\beta)^2} }$. Taking expectation over $q$, on the left hand side, we have the second moment of the subgradient, $\\mathbb{E}[\\Vert g_k \\Vert^2]$ . In (23)-(27), (line 903-906, in Appendix), it directly shows that the stochastic noise $\\hat{v}(q)$ is an upper bound of the  $\\mathbb{E}[\\Vert g_k \\Vert^2]$ and  $\\hat{v}(q)$ is minimized by the importance sampling distribution with weight $w^*$, as stated in Theorem 1.\n\nFor per-iteration loss variance reduction, we consider a $\\theta_k$, the model parameter at the $k$-th iteration and corresponding dual form objective is given as $F_{\\beta}(\\theta_k, \\alpha_k) = \\alpha_k + \\frac{1}{1-\\beta}\\mathbb{E}[(\\frac{p(x)}{q(x)}(\\ell(\\theta_k;x)-\\alpha_k)^{+})]$. Then it is straightforward to see that the variance of this estimate is reduced if: $\\mathbb{E}[(\\frac{p(x)}{q(x)})((\\ell(\\theta_k;x)-\\alpha_k)^{+})^2] < \\mathbb{E}[((\\ell(\\theta_k;x)-\\alpha_k)^{+})^2]$. Considering the pretrained model loss-based importance sampling distribution $q(x) \\propto \\varphi(\\ell(\\theta_0;x))p(x)$, we have $\\mathbb{E}[\\frac{Z((\\ell(\\theta_k;x)-\\alpha_k)^{+})^2}{\\varphi(\\ell(\\theta_0;x))}] < \\mathbb{E}[((\\ell(\\theta_k;x)-\\alpha_k)^{+})^2]$ where $Z$ is the normalizing constant. (Informal statement: Intuitively, the result suggests that if instances with high loss under $\\theta_0$ continue to have high loss during fine-tuning (i.e., $\\theta_k$), then the importance sampling concentrates on high-loss regions, thereby reducing variance. As discussed in [R2A3], this assumption can be reasonable in the context of fine-tuning from a well-initialized model, and high-loss-inducing samples often require multiple optimization steps to be effectively addressed in risk-averse training.)\n\nWe will incorporate this discussion and explanation into the revised manuscript. Thank you again for your constructive suggestion.\n\n\n---\n\n**[R3Q3]**  (Q3, W7) While the illustrations are very well done, the choice of competing algorithms is not very well justified....  / Can the authors explain how they chose the other methods they compared to? \n\n**[R3A3]** \nThank you for this question. In our results table, SGM uses the same configuration but without importance sampling. This isolates the contribution of our pretrained-model loss guided importance sampling scheme and demonstrates the benefit. We selected DORO and $\\chi^2$-DRO to assess whether state-of-the-art robust optimization methods can address the tail-risk challenges without our proposed mechanism- i.e., importance samples. The results highlight that such methods do not inherently resolve the difficulties addressed by RAMIS, underscoring the need for our new approach. Finally, ERM is included as a conventional baseline to illustrate the limitations of average-risk optimization in high-risk scenarios. \n\nWe will clarify this motivation in the revised version.\n\n\n\n---\n\n**[R3Q4]** -   (W4) The overall idea hinges upon the assumption that the generative model is sufficiently good to generate high-risk data points when such high-risk data points are not present in the data. It would be best to formalize this, i.e., what generalization capabilities are assumed on the generative model for the overall approach to work...\n\n**[R3A4]**  As the reviewer notes, our framework assumes that the generative model can sample from the true distribution $p(x)$, including high-risk regions. This is feasible under our setup as we use a score-based generative model, where the input to our importance sampler is the time-dependent score $\\nabla \\log p_t(x)$. This implies that the model can generate samples following $p(x)$.\n\n We will formalize this assumption more clearly in the revised manuscript.\n\n---\n\n**[R3Q5]** (Q4, W3) CVAR is not the only risk-sensitive measure that could be used.... adequate estimation of tails are always at the core of distributionally robust learning even if some other risk measure than the CVAR is used / Can the authors try experiments using extremile rather than the CVAR?\n**[R3A5]** We appreciate the reviewer's suggestion. Our framework is indeed general and can be applied to other risk measures.\n\nFollowing the Extremile formulation in [2] and the notations, we use: various $\\tau$ values raning from 0.5 to 0.99, $r(\\tau)=\\log(1/2)/\\log(\\tau)$, $K_{\\tau}(t) = t^{r(\\tau)}$, and $J_{\\tau}(F(x))$ which is scaled by the squared loss. We compare *RAMIS + Extremile* (our framework applied to Extremile with importance sampling) against naive Extremile optimization under the same experimental setup as in Figure 2 of the paper.\n\n| $\\tau$    | RAMIS + Extremile (mean ± std) | Extremile (mean ± std) |\n|------|---------------------------|------------------------|\n| 0.99 | **0.187 ± 0.144**             | 0.339 ± 0.207          |\n| 0.95 | **0.064 ± 0.021**             | 0.090 ± 0.044          |\n| 0.90 | **0.044 ± 0.015**             | 0.048 ± 0.021          |\n| 0.80 | **0.0288 ± 0.0062**           | 0.0289 ± 0.0041        |\n| 0.50 | **0.0158 ± 0.0015**           | 0.0179 ± 0.0025        |\n\nIn all settings, RAMIS with importance sampling outperforms the naive baseline, confirming both the method’s flexibility and effectiveness across different risk measures. We will include these new results in the revised manuscript.\n\n\n\n\n---\nWe appreciate the reviewer’s valuable feedback again. We believe we have addressed all concerns; if so, we kindly ask the reviewer to consider a higher score. We are happy to provide additional clarification if needed."}]

Author rebuttal:

Meta-review: This paper provides a new approach for optimizing conditional value-at-risk (CVaR) over distributions generated from diffusion-based generative models. It proposes an algorithm for reweighting the sampling distribution of the generative diffusion models and theoretically analyze the convergence of their approach. Reviewers liked the algorithm and believed that the idea is original and can offer potentially interesting venues in both theory and practice. The drawback of this paper is that the empirical evaluation is quite limited.

All reviewers suggested acceptance with 2 Accepts and 1 Weak Accept. AC follows consensus to accept the paper.
Decision: Accept (spotlight)