SONA: Learning Conditional, Unconditional, and Matching-Aware Discriminator
Authors: Yuhta Takida
Satoshi Hayakawa
Takashi Shibuya
Masaaki Imaizumi
Naoki Murata
Bac Nguyen
Toshimitsu Uesaka
Chieh-Hsin Lai
Yuki Mitsufuji
Venue: ICLR 2026 Poster (2026)
Keywords: Generative adversarial network
conditional generation
generative models
Primary area: generative models

Abstract: Deep generative models have made significant advances in generating complex content, yet conditional generation remains a fundamental challenge. Existing conditional generative adversarial networks often struggle to balance the dual objectives of assessing authenticity and conditional alignment of input samples within their conditional discriminators. To address this, we propose a novel discriminator design that integrates three key capabilities: unconditional discrimination, matching-aware supervision to enhance alignment sensitivity, and adaptive weighting to dynamically balance all objectives. Specifically, we introduce Sum of Naturalness and Alignment (SONA), which employs separate projections for naturalness (authenticity) and alignment in the final layer with an inductive bias, supported by dedicated objective functions and an adaptive weighting mechanism. Extensive experiments on class-conditional generation tasks show that SONA achieves superior sample quality and conditional alignment compared to state-of-the-art methods. Furthermore, we demonstrate its effectiveness in text-to-image generation, confirming the versatility and robustness of our approach.

Published as a conference paper at ICLR 2026
SONA: LEARNING CONDITIONAL, UNCONDITIONAL, AND MATCHING-AWARK DISCRIMINATOR
Yuhta Takida' Satoshi Hayakawa" Takashi Shibuya' Masaaki Imaizumi Naoki Murata' Bac Nguyen' Toshimitsu Uesaka' Chieh-Hsin Lai Yuki Mitsufuji'- 'Snyy AI, 2Sny Group Corporation, 3The University of Tokyo
ABSTRACT
Deep generative models have made significant advances in generating complex content, yet conditional generation remains fundamental challenge. Existing conditional generative adversarial networks often struggle to balance the dual objectives of assessing authenticity and conditional aligmment of input samples within their conditional discriminators. To address this, we propose novel dis- criminator design that integrates three key capabilities: unconditional discrimi- nation, matching-ave
supervision to enhance alignment sensitivity, and adap- tive weighting to dynamically balance all objectives. Specifically, we introduce Sum of Naturalness and Alignment (SONA), which employs separate projections for naturalness (authenticity) and alignment in the final layer with an inductive bias, supported by dedicated objective functions and an adaptive weighting mech- anism. Extensive experiments
condiionndii generation tasks show that SONA achieves superior sample quality and conditional alignment compared to state-of-the-ard methods. Furthermore, we demonstrate its effectiveness in text-to- image generation, confirming the versatility and robustness of our approach.
INTRODUCTION
Deep generative modeling has achieved remarkable progress in synthesizing images (Podell et al. 2024 Esser et al.) 2024), audio (Novack et al. 2024 2025), and video (Yang et al., [025] Polyak al. 2024 Kong et al.] [2224] Wan et al. 2022), Nevertheless, generating high-quality samples that are well-aligned with conditional information, such as class labels or text prompts, remains a central
challenge (Ho & Salimans 2021 Dhariwal & Nichol 2021 Liu et al. 2023 Zhang al. 2024
Generative adversarial networks (GANs) (Goodfellow et al. 2014) have been instrumental in ad- vancing conditional generation, with much of the research focusing on the design of conditional dis- criminators (Kang et al.] (202a)). The task of the conditional discriminator is typically decomposed into two sub-problems: distinguishing real from generated samples (unconditional discrinination) and assessing conditional alignment. This decomposition can be naturally motivated by the likeli- hood factorization of the joint distribution, p(z, 3) ply (z)). where x is data sample and y is a conditioning variable.
Two main approaches have emerged based on this factorization. The classifier-based approach, pio- neered by AC-GAN (Odena et al. 2017). uses dual- heal discriminator to simultaneously evaluate sample authenticity and label alignment (Gong et al. 2019 Hou et 2022: Kang al.) 202T). The projection-basee approach, introduced by Miyato & Koyama (2018). models the discriminator as sum of unconditional discrimination and alignment terms, eliminating the need for auxiliary clas- sifiers and thereby simplifying the architecture. This simple yet effective design has been widely adopted in modern conditional GANs as the de facto standard without major modifications (Brock)
et al. 2019 Karras et al., 2019 2020b 2021 Sauer et al., 2022 2023 Huang al. 2024).
Despite these advances, conditional discriminators still face the fundamental challenge of balancing the dual objectives of unconditional discrimination and conditional alignment (Reed et al.) 2016 Hou et al.] 2022). Classifier- methods require careful tuning of weighting coefficients to achieve this balance (Kang et al.] 202T). We also suspect that projection-based methods may not

---

Published as a conference paper at ICLR 2026
Table 1: Three desiderata for our proposed method, SONA.
Conditional discrimination
(i) Unconditionl disc.
(ii Matching-awan disc.
(iii) Adaprive weighting (Section 3.3
Capabilities
(Section 3.1
(Section 3.2
Classificr-based
Projection-hased
N/A
SONA (ours)
(Section
(Section 4.3
(Section
fully exploit the likelihood decomposition for the unconditional discrimination task, as discussed in Section 3
To address this issue, we aim at a discriminator design that incorporates three capabilities, as sum- marized in [able First, introduce (i) unconditional discrimination robustly distinguish real from fake samples, independent of the condition. Second, we enhance the discriminator 's sensitivity conditional alignment by providing additional supervision through mismatched (negative) sam- ples, resulting in a (ii) matching-aware discriminator (Reed et al. 2016; Zhang et al. 2017 Tao
al. 2023; Kang et al., 2023b). Third, we employ an (iii) adaptive weighting mechanism to dy- namically balance the objectives of conditional, unconditional, and matching- aware discrimination.
Specifically, we introduce Sum of Naturalness and Alignment (SONA), novel method that simul- taneously fulfills all the capabilities listed in Table | as detailed in Section 4 Our discriminator is designed with separate projections to independently assess input naturalness (authenticity) and con- ditional alignment, while incorporating effective inductive bias to support both tasks efficiently. To fully leverage this architecture, we propose a set of objective functions for training conditional, unconditional, and matching aware discrimination, and validate their effectiveness both theoretically and empirically in Section 5) Additionally, we introduce a simple yet effective adaptive weighting mechanism for these three discrimination tasks, enabled by our carefully designed loss functions. In Section 6 we evaluate SONA on image datasets with class labels, demonstrating that it generates higher-quality samples with better conditional alignment than state-of-the-art (SoTA) discriminator conditioning methods. We further extend our experiments to text-to-image generation, showing the applicability of SONA to more complex conditioning scenarios.
PRELIMINARIES
Let Pdaa (z. y) represent the data distribution, where E X is data sample and y Y is the conditional information describing the corresponding x (e.g., class label or text prompt). Our objective is to learn the conditional distribution from finite set of samples drawn from it. For this purpose, a trainable generator is introduced, denoted as inducing the generator distribution, denoted as Py (xr ly). In one of the standard GAN setups, the generator is parameterized a function that transforms a tractable noise (c.g., a Gaussian noise) to data sample as Z x Y + X, where 0 indicates a set of parameters modeling the generator and
is the noise; thus a sample drawn from Py (-ly) is obtained by Ig go(2. y) with a noise drawn from base distribution: 2 Pz- Hereafter, we use V and to denote maximization and minimization objectives, respectively.
2.1 GENERATIVE ADVERSARIAL NETWORKS
We review the formulation of GANs and introduce the sliced Wasserstein perspective to present the concept of optimal projection for unconditional discrimination. The problem setup described above includes unconditional generation tasks by setting y null conditioning. In this subsection, we omit y from the formulations for simplicity.
GANs. In GANs, discriminator, denoted as X RR, is introduced, which is expected to discriminate between the samples drawn from the data and generator distributions with its scalar outputs. GAN formulates the optimization problem to make the generator distribution closer the data distribution by solving a minimax problem:
max (fig(fig),
and
min JaAN f).
Here, the variables following the semicolons are held fixed during each optimization step, and will omit such variables when the context clear. The specific forms of VGNN and JGAN depend on the chosen GAN variant or loss (see Appendix B.T more details).
2

---

Published as a conference paper at ICLR 2026
Sliced Wasserstein perspective GANs. Typical discriminators be represented as f(x) (wo, h(x)), where h X + RR, w E 8P-1, and (.-.) denotes the Euclidean inner product. Takida augmented Sliced Wasserstein approach (Kolouri et al. 2019 Chen et al. 2022) with a single direction (w). Building on this interpretation, they pro-
et al. (2024) interpreted this formulation
pose encouraging optimality in the sliced Wasserstein sense the normalized projection, resulting in slicing adversarial networks (SANs): max VSAN(w, h) and ming JSAN (g), where
VSAN(W: h) Bepaa(t) (x) (w) (1(h( p2, sg)))) + VGAN VcAN((sg(w),,)) (g) - (o)) [ww, (ar)),,
where s-(-) denotes the stop-gradient operator" The first two terms in VSAN encourage the direc- tion w to maximize the sliced Wasserstein distance given by h. Intuitively, the learned direction is expected to optimally distinguish real and generated samples in the feature space defined by h. See Appendix B.2 for more detailed explanation of the aforementioned perspective.
2.2 CONDITIONAL GANS
Most conditional GANs employ either classifier- based or projection- based approaches. To illustrate the core concepts, briefly review AC-GAN a representative classifier- approach, well as the projection-based approach. A detailed review related work is provided in Appendix [A]
In conditional generation settings, the discriminator is modeled f X Y + R. enabling it to distinguish between the two conditional distributions, Pauma Paam(>ly) and Py (xly). For simplicity, we assume Y is discrete space in this subsection.
Classifier-based approach. Odena et al. (017) introduced AC-GAN, which combines the original GAN losses (i.e., VGAN and JGAN) with cross-entropy classification losses: VCLS (pan(z..) [log C(z, y)] and JCLS = -Bp, (x.y) [log Czz, v)] to optimize the discriminator and gener- ator. The auxiliary classifier typically defined as C(r, y) softmax,, ((.fesss (z, y)lver /T), where Fas: : X Y + IR and r E Ry a temperature. Notably, under this setup, the maximization loss VeLs is equivalent to the InfoNCE loss (Oord et al., 2018):
Ven (Fan) = (a (x.3) log exp(Jen(x,)) 9)/T)
(4)
Eepa((y)) exp (x,, y/ s/)/T)
To enable the discriminator to predict class labels, fas(I, y) is further parameterized using the dis- criminator's 's deep feature and additional learnable embeddings wyy E TR. as fa, v) (wy. h(x))-
Projection-based approach. Miyato & Koyama (018 proposed a simple yet effective discrim- inator design. Based on the Bayes-rule-based log-likelihood-ratoo factorization, they implement the discriminator as a sum of conditional and unconditional terms: f(z, y) = fi (a, y) + f2(2) = (wy, h(z)) + (h(x))) where, by abuse of notation, wy, denotes the embedding of y, and 1 is learn- able function. For efficient optimization, the intermediate feature h(x) is shared between f1 (x, y) and fz()). In practice, is usually parameterized as linear layer, reducing the discriminator
f(, v) = (wyy Mx))) + (w, Mxx)) + b,
(5)
where b E IR is learnable bias. This approach does not require any modifications other than the projection discriminator, such as optimization schemes or objectives. widely used its original form, and we hereafter refer to the broad class of GANs based on this approach simply as PD-GANs.
3 MOTIVATION: KEY CAPABILITIES OF CONDITIONAL DISCRIMINATOR
In this section, we raise the desirable capabilities for our discriminator, and discuss whether the ex- isting classifier- and projection-base approaches satisfy these criteria (see Table T for a summary).
For any function U X R. (xy(t) Ux)) is equivalent to ( (g((,, =)}] and is therefore differ- entiable with respect to g. We adopt the former notation for simplicity throughout this manuscript.
3

---

Published as a conference paper at ICLR 2026
3.1
UNCONDITIONAL DISCRIMINATION
We argue that unconditional discriminator learning is essential even in conditional generation tasks, as existing approaches decompose the role of the conditional discriminator into unconditional dis- crimination and evaluation of conditional alignment. masssifier-based discriminators inherently sup- port unconditional discrimination by explicitly employing the unconditional GAN loss (see Sec- tion 2.2 In contrast, projection-based discriminators, when used with standard GAN losses, may not provide this capability, as discussed below.
Projection-based discriminators as shown in Equation 5 and are thus inherently capable of modeling unconditional discrimination.
equipped with both unconditional and conditional projections,
However, since Equation (5) can be rewritten as (wy h(z)) with Wi By + E RR, the generator is optimized by ming [GAN(9: (my, h(x)) + b), essentially with a y-dependent projection iyy This suggests that, with this parameterization, the objective functions typically used in PD-GANs may not fully leverage unconditional discrimination.
3.2 MATCHING-AWAR DISCRIMINATION
We next highlight the importance of enhancing the discriminator's sensitivity to conditional align- ment by incorporating negative samples, following the approach of[Reed et al. (2016). Specifically, to encourage conditional alignment, they proposed using negative samples that are realistic but as- sociated with incorrect class labels, thereby mismatching the conditional information.
As shown in Equation 4. AC-GAN can be interpreted as implicitly utilizing such negative samples drawn from the product of marginals, i.e., (x. ~ Paltaa (2) (a))Ptaa(//)) in its cross-entropy loss, in addition to samples from the true joint distribution Pduta (2,, y). This advantage is formalized in Proposition [ which implies that the cross-entropy loss induces the discriminator feature to be y- extractable, sensitive conditional alignment, under the assumption that Pdma(y) is uniform. This proposition imposes the uniform assumption on Pdaa (V), which holds for well-constructed image datasets (Krizhessky et al. 2009: Russakovsky al. 2015), where each class contains the same number of samples.
Proposition (Log conditional probability maximizes VeE). Assume Piaa(y) is a constant re- gardless of y E Y, e.g., a uniform distribution. The function f maximizes Ven if f(x, y) = log Pdata (y] ()) + (x) for an arbitrary function rx :X- R.
While classifier-based approaches (including but not limited AC-GAN) employ classification losses similar or analogous to InfoNCE, projection-base GANs do not incorporate such losses, resulting in the absence of explicit mechanisms for inducing matching-awareness..
3.3 DESIDERATA OF OUR DISCRIMINATOR
Classifier-based GANs possess the two additional discrimination capabilities outlined in the pre- vious subsections, while most PD-GANs do not. However, key advantage of PD-GANs is that they avoid introducing additional hyperparameters that require manual tuning, which is beneficial for practitioners. In contrast, our goal is to propose novel conditional discriminator that integrates both unconditional and matching-awan discrimination into the training process, while adaptively balancing these different objectives. A summary of these comparisons is shown in Table [
PROPOSED METHOD: SONA
To achieve the desiderata presented in Section 3 we design the discriminator and propose a set of maximization objective functions for it. We provide theoretical and empirical support for our
method in Section 5
We formalize the training procedure of SONA in Algorithm of Appendix C
4.1 DISCRIMINATOR PARAMETRIZATION
Inspired by the projection discriminator (Equation (5), we design the discriminator to evaluate sam- ple inputs by summing scalar terms for (a) the (unconditional) naturalness, i.e., distinguishing
4

---

Published as a conference paper at ICLR 2026
Alignment (ttg)
Alignment wul l'w)
R
RD
BTT
VCR
BT-m
Real
Fake (P₂)
Naturalness (18)
Conditional
Naturalness (w)
(Pana)
likeliness
VGAN
Posilive
VGAN
VSAN
(p(ll))
(a) AC-GAN
PD-GAN
(c) SONA
Negative
Figure I: Comparison of SONA with existing classifier- and projection- based methods for discrim-
inator optimization. Our approach enables independent assessment of sample naturalness and align- ment, supported by the proposed inductive bias (Section 4.1 and objectives (Sections and
real from fake samples, and (b) the alignment with the conditioning information. To achieve this compositional modeling, we introduce a feature extractor X + IR&,, shared across both tasks (here, consistent with the notation in Section 2). The extracted features h(x)) are then projected onto independent directions w E SD-1 and wy E SD - for each Y as follows.
For naturalness, we simply project the feature onto w. For conditional alignment, we incorporate an inductive bias based on the hypothesis that assessing naturalness and conditional alignment are or- thogonal tasks. From an optimization perspective, optimizing the generator for aligmment should not interfere with optimizing it for naturalness. To encode this inductive bias, we define the alignment term using an orthogonal projection: (Wy, IT (x))) where TI [()) hx)) (w, hwr)).
Thus, our discriminator is parameterized as the sum of these two terms
f(x, v) = (w, h(z))
(Wyy llwm(()))
(6)
foy (ar): Naturalness
f (2, g): conditional Aligmment
where dN {w> h). 4 [ww hy. h}. In this formulation, we expect to be responsible for distinguishing the naturalness of input samples (as in Section 4.2), while wy focuses on conditional alignment (as in Section 4.3). Here, we can optionally add a bias b E to the naturalness term, which can also be absorbed into h. Please also refer to Figure for an illustration of our strategy.
4.2 UNCONDITIONAL LEARNING
To address the first desideratum in Table we formulate a minimax problem that encourages the naturalness term in Equation (6) to distinguish between real and generated samples independently of (see Proposition in Section 5.I). We employ SAN objective functions to learn the optimal w for unconditional discrimination, specifically using Equations (2) and (3) the minimax objectives:
max (w, h), and min Js) 4N
(7)
Note that only the parameters associated with the naturalness term fN Equation (6) are included; 4 2N = {w,). which is used only for conditional alignment, is not involved. This optimization ensures that focuses on determining whether an input sample originates from the data or the gen- erator, as intended. We denote VSAN
(w, (w,h) h) as VSAN (xx in Equation (12 for a unified formulation.
4.3 LEARNING CONDITIONAL ALIGNMENT
Next, we develop based learning for the conditional alignment, building on the w-based uncon- Specifically, introduce additional objective terms to
ditional learning described in Section 4.2 enable our discriminator to perform conditional discrimination and to be aware of the mismatch, the latter corresponding the second desideratum in Table
To achieve this, we incorporate the Bradley- Terry (BT) model (Bradley & Terry 1952 reviewed in Appendix B.3), which is widely recognized for its efficiency in modeling pairwise comparisons and
5

---

Published as a conference paper at ICLR 2026
has recently been applied in reinforcement learning from human feedback (Rafailov et al. 2023 For each pair of samples, we denote the preferred sample as the "winning" sample Tw and the less preferred as the "losing" sample Ig. response for condition y. The model defines the prob- ability that Tee is preferred over xy given y using evaluation function f X Y R as Pr( is preferred over srlyy) a (f( v) f(xr, where x()) denotes the sigmoid function. Following standard practice, we optimize our discriminator f by maximizing the following likeli- hood:
VET Bur me (J y) ((re,))))]
In our framework, samples drawn from the true joint distribution Pdam (2, y) are always designated as the winning samples Zws since this distribution represents the target. For the losing samples It, consider two distinct distributions, resulting in two additional objectives, follows.
BT-C loss for conditional discrimination. The first losing distribution the generator distribution. From Equation (8), the corresponding BT loss is
VBBTe(ff Epau(y) (y)a((a (sell)) log ar (gg( (Iw) + fa, (Iww v) - ((e( f (ze, v))l
(9)
This BT loss compares real and generated samples conditioned on given y, thereby measuring conditional dissimilarity. The sum of the first two terms corresponds to [Io,, y), while the latter two correspond to f y)- Notably, since the objective her is to learn conditional alignment, the parameters & A are optimized only through the alignment term f while the naturalness term f is frozen by applying the stop-gradient operator solely to the naturalness term. Under optimality assumptions, including those related to Equation (9). Equation (9) can be interpreted as a specific divergence between Ponaa (xly)) and py (xly),, up to constant, as shown in Proposition of Section 5.1
BT-M loss for matching-aware discrimination. The second losing distribution, chosen address the second desideratum, is the marginal data distribution, which ignores the given condition y- This helps the discriminator identify samples that do not satisfy the specified condition, even if they are real samples. The corresponding BT loss is
VBT.M (eonaliipaattsu/lbuuaaaa Dlg o (J (Zgg(())(( + få (I v) (x)( f (x w))l (10)
This BT loss compares data samples aligned with the condition y against negative samples drawn from the marginal distribution, analogous to matching loss. As shown in Proposition 3 of Sec- tion 5.J] maximizing Equation (IO) with respect to the discriminator yields the log gap between the
conditional and unconditional probabilities. log Paata (xly) - log Pdata (z), which is useful for enhanc-
ing conditional alignment (Ho & Salimans 2021 Chen et al. 2025b).
Minimization optimization for conditional alignment. Finally, introduce minimization ob- jective for generator optimization with respect to conditional alignment. By swapping the data and generator distributions in Equation (9). obtain minimization loss analogous to that used in 2018):
relativistic pairing GAN (Jolioeur-Martinnee
(B) = (M) (am 3) [log a (f (Ieala)) + fa, (Tg. - fu (ma) f& (za, B))l
(11)
Here, slight modification is added: as in Equations and (10,, the stop- soopggradient operator is applied only in the naturalness term (note that the third term does not include g), ensuring that minimization occurs orthogonally to the direction represented by (see the orthogonal operator in Equation (6). This approach allows the loss to specifically enhance the conditional alignment of generated samples along wyy while authenticity is enforced by JSAN using the direction responsible for unconditional discrimination. Therefore, minimizing JSAN and JBT-C does not cause interfer- ence, enabling each objective address its respective aspect independently.
4.4 OVERALL OBJECTIVE FUNCTION WITH ADAPTIVE WEIGHTING
We have introduced the maximization and minimization objective terms in Sections 4.2 and 4.3 The overall objective for training our GAN is summarized follows:
max VSAN(#N) + ()rcc(f))) + (f and min JSAN(9) + JBTe(O). uUU
(12)

---

Published as a conference paper at ICLR 2026
To ensure adaptive balance among the maximization objective terms VSAN, VET-C. and VETTM- introduce learnable scalar parameters. Specifically, we first adopt VOAN from Goodfellow et al. (2014) to construct VSAN. which is formulated with log (-)) (see Appendix B. We then replace logo (4) in each of VSAN. VBTC. and VIT with log (s 1)/s, where 8 E 1R>g is learnable. To prevent these coefficients from diverging. we constrain them such that SSAN + * $BT-c + & 1. This approach makes the adaptive weighting possible by incorporating the current situation during E.4 for details), thereby satisfying the third desideratum in Table
training (see Appendix E.4
Adaptive weighting has been investigated in general multi-task learning (Kendall et al., 2018). How- ever, these approaches are not specifically designed for GAN training, so they may not be suitable for our purpose. In particular, we hypothesize that the unbounded nature of the coefficients in these ap- proaches can be harmful to GAN training, as GANs are highly sensitive to the learning rate (Heusel et al. 2017). This hypothesis motivates the development of our adaptive weighting mechanism. To empirically validate our hypothesis and demonstrate the effectiveness of our method, we compare with the approach proposed by Kendall et al. (2018), using the same experimental setup described in Section 6.3 Our method achieves an FID of 5.65 and an IS of 9.51= which are significantly better than the baseline results of FID 16.62:t4.04 and IS 7.88+
5
ANALYSIS OF SONA
5.1
THEORETICAL GROUNDING FOR OUR MAXIMIZATION OBIECTIVES
In this subsection, we present propositions to demonstrate the validity of the objective terms intro- duced in Section and Section 4.3 Proofs are provided in the Appendix.
First, the following proposition, which is restatement of Theorem 5.3 in Takida et al. (2024), establishes that optimizing the generator and discriminator using the minimax objective functions from Section 4.2 enables unconditional GAN learning.
Proposition 2 (Informal; Unconditional discrimination by VSAN). Let the unconditional discrimi- nator (the naturalness term) be [N (x)) = (w:, M(x)) with w E RDD1 and : X + RRD. Under suitable regularity conditions for h, the objective JsAN(g; W, hi) is minimized only if g minimizes certain distance between Pasta (z) and Pg (z), where & = arg max,, VSAN(W, h)) for a given h.
Next, we analyze the BT-based objective functions introduced in Section 4.3 BT-C loss VBT-C com- pares samples from the dataset and the generator with specific conditioning. Under certain optimal conditions, this loss can represent the conditional dissimilarity between conditional distributions, as demonstrated in Proposition
Proposition 3 (Conditional discrimiantion by Ver-c)- Let the discriminator be J [x, y) (x)
(x, v). where (x(x)= (w, h(x)) with w E h X + RD, b E. and f ; X x Y + + R. Assume that the generator achieves (I()) Pama(a)), and and h maximize VSAN for given Panta and pq- If f maximizes Equation 13). then it is minimized if and only if pana pana(x Pa (yl)) for y E Y.
CuT- (ppsrs (w)p w/ [log (f (Iw) ( v) (x2) - (x (13)
Here, Equation [13 corresponds to the RHS of Equation 9 with generalized terms. We note that in our method, the conditional alignment term (f^ in this proposition) shares h and w with the naturalness term, a constraint not considered in this proposition. However, since minimizing VSAN enforces only one-dimensional constraint on lt given w, we expect f to have sufficient capacity even conditioned on "san-minimization. Thus, this proposition still offers valuable insights.
Finally, BT-M loss using samples from the marginal data distribution, VETM, can be interpreted as a contrastive loss comparing positive and negative data samples. Specifically, VBT-N is equivalent to an InfoNCE loss with single negative sample per positive sample in its denominator. The following proposition shows that this objective encourages the conditional discriminator to learn the log gap between conditional and unconditional probabilities, up to an arbitrary function independent of x:
Proposition 4 (Log gap probability maximizes VBT.M). The function ff maximizes VAT if fxx y) = log Paata (xl y) log Paan (1:) + TY (u) for an arbitrary function ry .Y - R.
7

---

Published as a conference paper at ICLR 2026
SONA
10"2
SONA wio Vart.m
A2 100-
PD-GAN
10"3
40
of modes (N)
# of modes (N)
# of modes (N)
Figure 2: Empirical study on MoG using Wasserstein-2 distance (W2), Conditional Wasserstein-2
distance (eW2), and the number of failure cases (NF). See Section 5.2 and Appendix F.T for details.
Real data
SONA
SONA w/o
PD-GAN
0.5
0.5
0.0
0.0
0.0
0.0
-0.5
-0.5
-0.5
-0.5
0.5
Figure 3: Ground truth samples and generated samples from three baseline models. Different mark- ers and colors represent samples from distinct classes among the N 36 total classes.
Although Proposition 4 superficially resembles Proposition I in Section 3.2, there are two key dif- ferences. First, Proposition 4 does not require the uniform assumption on Pdaa (v), allowing it to be applied to broader settings, such as datasets with biased class distributions or text-caption-image datasets. Second, the extra term in the maximizer of Proposition f independent of x, unlike in Section 3.2 This means that the maximizer captures the score gap between the conditional and unconditional probabilities, which helps to emphasize conditional alignment.
5.2 EMPIRICAL VALIDATION OF OUR METHOD
To empirically evaluate the effectiveness of proposed method, conduct experiments on dimensional mixture of Gaussians (MoG) dataset, which enables both visualization and accurate measurement of generative performance, The experimental details are provided in Appendix [.]
We train three models on the MoG dataset, varying the number of Gaussians (i.e., classes), denoted as N: (1) SONA, (2) SONA without the matching loss VAT-M. and (3) PD- GAN. To quantitatively assess generative performance, we use three metrics: (a) Wasserstein- 2 distance (W2 (z).Pa()) (x)),, denoted as W2). (b) conditional Wasserstein-2 distance 1 >> W2 (.)). Ps (x) denoted as cW2), and (c) the number of failure cases (NF). N
A failure is counted if there exists n E [N] such that W (P (xlyn)) (P e, where is set to the standard deviation of the Gaussians.
As shown in Figure using five different random seeds, generators trained with SONA demon- strate robust performance, consistently outperforming the baselines when N 2 30. Notably, SONA achieves zero NE, while the other two methods increasingly fail N grows. Qualitative results for N = 36 are visualized in Figure 33] where PD-GAN fails to cover all modes. In contrast, SONA without the matching loss produces overlapping samples between classes, indicating diffi culty in distinguishing between them. This underscores the importance of making the discriminator matching- aware to better utilize conditional information (the second desideratum).
EXPERIMENTS
6.1 BENCHMARK ON CLASS- CONDITIONAL GENERATION TASKS
We conduct class-condition image generation experiments on CIFAR10 (Krizhevsky al. 2009), TinyImageNet (Le Yang 2015), and ImageNet (Deng et al. 2009), using the StudioGAN repos- itory (Kang et al. 2023a well-established benchmark for these tasks. As basclines, we select
two ttate-of-the--rt (SolA classifier-base methods, ReACGAN (Kang et al. 2021) and Contra-
GAN (Kang & Park 2020). well PD-GANs, which is among the most widely used approaches.
8

---

Published as a conference paper at ICLR 2026
Table 2: CIFARIO
Table 3: TinylmageNet.
Method
IS
Method
FID 4
1S
Dens
Cover
BigGAN backbone
ContaGAN
23.06:11.99
12,47:1.45
0.621:0.5
0.461005
162.6911..99
ContaGAAN
4.74:0005
9.794:0.0
ReACGAN
18.99
15.37:008
0.2020003
0.54
130.77::.22
REACGAN
4.940.10
9,844:00
PD-GAN
20.7741553 14.29:1111
0.701:005
0.884002
111.0743343
PD-GAN
4.602005
9.874:006
SONA
16.3344022
16.60-10.35
0.74
0.59 4001
108.75+:0.00
SONA
4.24:0.07
10.08:10.03
Apply DigAMg
StyleGANZ borkhome
ComtraGAN
11.862032
16.01
0.78:002
0.6322011
142.07
ReACGAN
3.3920033
10.3320005
ReACGAN
9.93-0.34
20.25::0007
0.8:000111
0.09
301.31
PD-GAN
4.0610019
10.09110.05
GAN
13,0941000
16.57:40.4
0.784002
0.70+002
25.62-4:227
SONA
3.38-0.14
10.45+0.088
SONA
7.7620.29
23.00:1:110
0.99:0.01
0.79
82.23::0048
For evaluation, we use Frechét Inception Distance (FID) (Heusel et al.) 2017). Inception Score
(IS) (Salimans et al. 2016), Density & Coverage (Nacem et al. 2020). intra FID (Miyato & Koyama 2018 iFID) that is the average of class-wise FID.
We first train SONA on CIFARIO, and report the results in Table We evaluate both Big- GAN (Brock et al. 2019) and StyleGAN2 (Karras et al. 2020b) backbones. The results show that SONA consistently achieves the best performance across all metrics.
Next, we scale up the empirical evaluation by increasing both the image resolution (64x64) and the number of classes (200) using TinylmageNet. As shown in Table 3 SONA outperforms the other SoTA models on all metrics. Notably, SONA also benefits from DiffAug (Zhao et al. 2020p, leading data augmentation technique, achieving the best overall scores.
Finally, we evaluate SONA on the Ima- geNet dataset at a resolution of 128x 128. We use the BigGAN backbone, as it is the only architecture among single-stage gen- eration pipelines capable of producing rea- sonable images on the dataset. We com- pare performance under two batch size set- tings (256 and 2048), with results summa- rized in Table 4 According the table, SONA outperforms other methods on all metries except Density, Additionally, we compute Top-1 and Top-5 classification accuracies for the 1,000 ImageNet classes using an Inception V3 network, following Kang et al. (2023a). The results indicate that images generated by SONA align best with the conditioning class among all baselines.
Table 4: ImageNet.
Method
FID
IS
Dens f Cover 1 iFD
1op-1/5 acef
Butch 250
CommaGNN
31.73
23.93
0.57
0.28
169.65
0.02/0.09
ReACGAN
18.73
51.29
0.85
0.46
131.83
0.20/ 00.88
PD-GAN
29.76
27.17
0.45
0.35
119.07
0.24 / 00.48
SONA
13.17
83.33
0.79
0.59
74.33
0.62 / 0.87
size
2048
ReACGAN
8.44
103.07
1.04
0.71
87.77
0.51/0.83 70.82
PD. GAN
8.85
96.11
0.95
0.81
52.65
0.63 / 0.83
SONA
140.14
48.45
0.80 0.93
Table 5: Text-to-image generation tasks on CUB and COCO.
CUR Wah et
201
COCO (Tin
2014
Method
FID
CLIP Score 1
FID J.
CL.IP Score
GALIP (original: concal)
11.76
0.3310
5.30
0.3639
GALIP SONA
10.20
0,3342
4.70
0.3677
Table 6: Text-to-image generation task under zero-shot setting on COCO. GALIP and GALIP SONA trained on CC12M, while the other basclines are trained on larger-scale datasets.
Method
Type
Param size (B)
Data size
zFID 4
CLIP Score
Speed
LDD Rombach et al
2022
Diffusion
1.45
400
12.63
3.7
GLIDE
Nichol el al.
Dillusion
5
250
12.24
15.0
DALLEE
Kamesh
2022
Diffusion
6.5
250
10.39
Imagen Sahana et al 2022
Diffusion
7.9
860
7.27
9.1
InstaHlow (LiU
Flow
0.9
13.10
0.09
StyleGAN- T
(Sauer el 2023
GAN
1.02
250
13.9
0.10
GALIP (original. concat)
GAN
0,24+0.08
12
13.78
0.3300
0.04
GALIP SONA
GAN
0.24+0.08
12
12.43
0.3411
0.04
6.2 BENCHMARK ON TEXT-CONDITIONAL GENERATION TASKS
We demonstrate the applicability of SONA to text-to-image generation tasks. Our experiments based on GALIP (Tao et al. 2023), which we verified to be reproducible using the official reposi- tory? The GALIP discriminator consists of frozen pre-trained CLIP encoders and learnable mod-

---

Published as a conference paper at ICLR 2026
ules. Text conditioning is performed by concatenating image features and text embeddings from the CLIP encoder, followed by processing with a shallow network. We apply SONA to the discriminator in straightforward manner, using the frozen CLIP text embedding for wy without modification. To assess the effectiveness of the proposed method, we train both the original GALIP and the SONA- based GALIP CUB (Wah et al. 2011]. COCO (Lin et al. (014), and CC12M (Changpinyo al., 2021), respectively. For models trained on CC12M, we report zero-shot performances on COCO. As shown in Table 5 and Table 6 SONA achieves improved FID scores while maintaining comparable text alignment to the original GALIP on three standard image datasets at 256x256 resolution. We suspect that our method reduces interference between the assessment of naturalness and alignment, even with fixed wyy. Adopting learnable wy for further improvement in CLIP score is left for future work. For reference, we also include other text-to-image models, not limited to GANs, in Table 6 Although these models differ in dataset scale and a direct comparison is not strictly fair because GALIP is trained on the smallest dataset, the table indicates that SONA applied to GALIP achieves competitive generation performance with the fastest inference speed among the listed models.
Table Ablation study using CIFARIO
6.3 ABLATION STUDY
Adaptive weighting
Orthogonal
matching loss VISTS
pooj. Eq. 1
FID
1S
We evaluate the contribution of each pro- posed component in SONA by training models on CIFAR10 using the PyTorch of- ficial codebase provided by Broock et al. 2019). Results are summarized in Ta-
7.51+0.14
0.29
9.14
6.02:20228
9.54
5.65
9,51
7.09
9.52+0007
ble 7 Orthogonal modeling in få, (ar, y) improves the generation performance in FID, while the
BT-M loss VATA does in IS. By adopting both, SONA achieves better generation performance in terms of both FID and IS. In contrast, we can also see that the adaptive scaling coefficients intro- duced in Section 4.4 work.
6.4 DISCUSSION ON COMPUTATIONAL TIME
Table 8: Training efficiency (iteration/min).
We report the computational efficiency of each base- line in Table 8 based on the experiments described
Method
CIFARID
TinyIN
ImugeNNt
ContraGAN
360.36
129.87
80.70
in Section 6.1 PD-GAN demonstrates the high-
ReACGAN
322.15
107.23
78.84
PD-GAN
442.80
195.76
101.91
est training efficiency. attributable to its simple de- sign. Nevertheless, SONA achieves comparable ef- ficiency PD-GAN and surpasses other state-of-the- art classifier-based methods. Additionally, we illus- trate the training convergence behavior on ImageNet (with batch size of 2048) in Section 6. as shown in Figure 4 We observe that SONA attains FID scores similar to PD-GAN for approximately the first three days, after which SONA exhibits a clear improve- ment, achieving lower FID scores. This performance gain justifies the additional computational overhead of SONA compared to PD-GAN.
SONA
410.95
169.13
90.16
340
10a
320
10g
12) MM
Training (day)
Figure 4: Behavior of training convergence: FID (L) and IS (t) as a function of training time (in days).
7 CONCLUSION
In this paper, we introduced SONA, a novel discriminator framework for conditional GANs that effi- ciently evaluates both sample naturalness (authenticity) and conditional alignment, while adaptively balancing unconditional, conditional, and matching-awas -wwae discrimination objectives. Experiments on image datasets demonstrate that generators trained with our method produce higher-quality sam- ples that more accurately aligned with the given labels compared to state-of-the-are methods. Additionally, we showed that SONA is applicable to text-to-image generation scenarios.
10

---

Published as a conference paper at ICLR 2026
ETHICS STATEMENT
Because our work involves training Al models that can generate synthetic content, there are inherent risks of producing harmful inappropriate outputs, such as deepfake images, graphic violence, offensive material, or content that may infringe on copyright. To mitigate these risks, it is essential to implement robust content filtering and moderation measures to prevent the creation of unethical, harmful, or infringing media.
REPRODUCIBILITY STATEMENT
All experiments described in Section 6 were implemented using open-source repositories, which we confirm are reproducible by rerunning them. The datasets employed in this study are publicly available via their official sources. Detailed implementation procedures are provided Appendix F Additionally, provide codes supplementary material and outline our training procedure in Algorithm The proofs of our theoretical claims can be found Appendix.
LLM USAGE
Large Language Models (LLMs) were used for academic proofreading and assistance in writing the abstract. They also supported coding tasks, including debugging, resolving errors, and visualizing results, All research ideas and theoretical contributions were developed solely by the authors.
ACKNOWLEDGMENTS
We are grateful Yuya Kobayashi for assistance in ensuring the reproducibility of the GALIP code and to Masato Ishii for helpful comments during the preparation of this manuscript. We also acknowledge the anonymous reviewers for their valuable suggestions and comments.
REFERENCES
Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324 345, 1952.
Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. Proc. International Conference on Learning Representation (ICLR), 2019.
Soravit Changpinyo, Piyush Sharma, Nan Ding, and Radu Soricut. Conceptual 12m: Pushing web- scale image-text pre-training to recognize long-tail visual concepts. Proc. IEEE/CVF Confer- on Computer Vision and Pattern Recognition (CVPR), 2021.
Dar-Yer Chen, Hmrishav Bandyopadhyay, Kai Zou, and Yi-Zhe Song. Nitrofusion: High-fidelity single-step diffuuson through dynamic adversarial training. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 7654-7663, 2025a.
Huayu Chen, Hang Su, Peize Sun, and Jun Zhu. Toward guidance-free visual generation via condition contrastive alignment. In Proc. International Conference on Learning Representation (ICLR), 2025b.
Xiongjie Chen, Yongxin Yang, and Yunpeng Li. Augmented sliced wasserstein distances. In Pruc. International Conference on Learning Representation (ICLR), 2022.
Casey Chu, Kentaro Minami, and Kenji Fukumizu. Smoothness and stability in GANs. In Pruc. International Conference on Learning Representation (ICLR), 2020.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hier- archical image database. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 248-255. leee, 2009.

---

Published as a conference paper at ICLR 2026
Prafulla Dhariwal and Alexander Nichol. Diffusion models beat GANs image synthesis. In Proc. Advances in Neural Information Processing Systems (NeurIPS), volume 34, pp. 7780-8794, 2021.
Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, al. Scaling rectified flow transformers for high-resolution image synthesis. In Proc. International Conference on Machine Learning (ICML), 2024.
Jiaojiao Fan, Qinsheng Zhang, Amirhossein Taghvaei, and Yongxin Chen. Variational wasserstein gradient flow. In Proc. International Conference Machine Learning (ICML), volume 162, pp- 6215, 2022.
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanis- las Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy. levgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer. Pot: Python optimal transport. Journal of Machine Learning Research, 22(78): 1-8, 2021.
URL http::/ wttppppprp/pp.e.e....p... 20 451 htmml
Rémi Flamary, Cédric Vincent-Cuaz, Nicolas Courty, Alexandre Gramfort, Oleksii Kachaiev, Huy Quang Tran, Laurène David, Clément Bonet, Nathan Cassereau, Théo Gnassounou, Eloi Tanguy, Julie Delon, Antoine Collas, Sonia Mazelet, Laetitia Chapel, Tanguy Kerdoncuff, Xizheng Yu, Matthew Feickert, Paul Krzakala, Tianlin Liu, and Eduardo Fernandes Montesuma. Pot python optimal transport (version 0.9.5), 2024. TRLhttps.: /ttttts:://ittiee wtt.ttttthu.cc.oo http://htt....co/.cooooooo/////p PythonoT/POT
Yuan Gao, Yuling Jiao, Yang Wang. Yao Wang, Can Yang, and Shumkang Zhang. Deep generative learning via variational gradient flow. In Proc. International Conference on Machine Learning (ICML), pp. 2093-2101, 2019.
Mingming Gong, Yanwu Xu, Chunyuan Li, Kun Zhang, and Kayhan Batmanghelich. Twin auxilary classifiers gan. In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2019.
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Proc. Advances in Neural Information Processing Systems (NeurIPS), pp. 2672-2680, 2014.
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. GANs trained by a two time-scale update rule converge to a local Nash equilibrium. In Pruc. Advances in Neural Information Processing Systems (NeurIPS), pp. 6626-66317 2017.
Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021.
Liang Hou, Qi Cao, Huawei Shen, Siyuan Pan, Xiaoshuang Li, and Xueqi Cheng. Conditional gans with auxiliary discriminative classifier. In Proc. International Conference on Machine Learning (ICML), 2022.
Nick Huang, Aaron Gokaslan, Volodymyr Kuleshov, and James Tompkin. The GAN is dead; long live the GAN! A modern GAN baseline. In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2024.
Rie Johnson and Tong Zhang. A framework of composite functional gradient methods for generative adversarial models. IEFE transactions on pattern analysis and machine intelligence, 43(1):17- 32, 2019.
Alexia Jolicoeur-Martinaau. The relativistic discriminator: A key element missing from standard gan. arXiv preprint urXiv11807.00334 2018.
Alexia Mnlicoeur-Martinen On relativistic f-divergences. In Proc. International Conference on Machine Learning (ICML.,, 2020.
Minguk Kang and Jaesik Park. Contragan: Contrastive learning for conditional image generation. In Proc. Advances in Neural Information Processing Systems (NeurIPS), pp. 21357-21369 2020.
12

---

Published as a conference paper at ICLR 2026
Minguk Kang, Woohyeon Shim, Minsu Cho, and Jaesik Park. Rebooting ACGAN: Auxiliary clas- sifier GANs with stable training. In Proc. Advances Neural Information Processing Systems (NeurIPS), pp. 33505-23518, 2021.
Minguk Kang, Joonghyuk Shin, and Jaesik Park. Studiogan: taxonomy and benchmark of gans for image synthesis. IEEE Transactions on Pattern Analysis and Muchine Intelligence, 45(12): 15725-15742, 2023a.
Minguk Kang, Jun- Zhu, Richard Zhang, Jaesik Park, Eli Shechtman, Sylvain Paris, and Taesung Park. Scaling up gans for text-to-image synthesis. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10124-0014, 2023b.
Minguk Kang, Richard Zhang, Connelly Barnes, Sylvain Paris, Suha Kwak, Jaesik Park, Eli Shecht- man, Jun- Yan Zhu, and Taesung Park. Distilling diffusion models into conditional gans. In Proc. European Conference Computer Vision (ECCV), pp. 428 047, 2024.
Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative ad- versarial networks. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4401-4410, 2019.
Tero Karras, Miika Aittala, Janne Hellsten, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Train- ing generative adversarial networks with limited data. In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2020a.
Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyz- ing and improving the image quality of stylegan. Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 8110-8119, 2020b.
Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Alias-free generative adversarial networks. In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2021.
Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 7482-7491, 2018. 2018.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Proc. Interna- tional Conference on Learning Representation (ICLR), 2015.
Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, and Gustavo Rohde. General- ized sliced Wasserstein distances. In Proc. Advances in Neural Information Processing Systems (NeurIPS), volume 32, 2019.
Weijie Kong, Qi Tian, Zijian Zhang, Rox Min, Zuozhuo Dai, Jin Zhou, Jiangfeng Xiong, Xin Li, Bo Wu, Jianwei Zhang, et al. Hunyuanvideo: A systematic framework for large video generative models. arXiv preprint arXiv:2412.036033 2024.
Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
Yann Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 2 2015.
Jerry Li, Aleksander Madry, John Peebles, and Ludwig Schmidt. On the limitations of first-order approximation in gan dynamics. In Proc. International Conference on Machine Learning (ICML), pp. 3005-3013, 2018.
Shanchuan Lin, Xin Xia, Yuxi Ren, Ceyuan Yang, Xuefeng Xiao, and Lu Jiang. Diffusion adver- sarial post-training for one-step video generation. In Proc. International Conference on Machine Learning (ICML), 2025.
Tsung- Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Proc. European Conference Computer Vision (ECCV), 2014.
13

---

Published as a conference paper at ICLR 2026
Xingchao Liu, Xiwen Zhang, Jianzhu Ma, Jian Peng, et al. Instaflow: One step is enough for high- quality diffusion- eext-o--imaee generation. In Proc. International Conference on Learning Representation (ICLR), 2024.
Zhaoyan Liu, Noël Vouitsis, Satya Krishna Gorti, Jimmy Ba, and Gabriel Loaiza-Ganem, Tron: Translator networks for O-shot plug-and-play conditional generation. 2023.
Lars Mescheder, Sebastian Nowozin, and Andreas Geiger. The numerics of gans. In Proc. Advances in Neural Information Processing Systems (NeurIPS), volume 30, 2017.
Mehdi Mirza and Simon Osindero. Conditional generative adversarial nets. arXiv preprint arXiv:1411.178. 2014.
Takeru Miyato and Masanori Koyama. cgans with projection discriminator. In Proc. International Conference on Learning Representation (ICIR), 2018.
Muhammad Ferjad Naeem, Seong Joon Oh, Youngjung Uh, Yunjey Choi, and Jaejun Yoo. Reli- able fidelity and diversity metrics for generative models. In Proc. International Conference on Machine Learning (ICML), 2020.
Vaishnavh Nagarajan and J Zico Kolter. Gradient descent GAN optimization is locally stable. In Proc. Advances in Neural Information Processing Systems (NeurIPS), volume 30, 2017.
Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, Ilya Sutskever, and Mark Chen, GLIDE: Towards photorealistic image generation and editing with text-guided diffusion models. In Proc. International Conference on Machine Learning (ICML), 2022.
Zachary Novack, Julian McAuley, Taylor Berg- Kirkpatik,, and Nicholas J Bryan. Ditto: Diffu- sion inference-time t-optimization for music generation. In Proc. International Conference on Machine Learning (ICML), 2024.
Zachary Novack, Ge Zhu, Jonah Casebeer, Julian McAuley, Taylor Berg- Kink-Kirkaa and Nicholas Bryan. Presto! distilling steps and layers for accelerating music generation. In Proc. International Conference on Learning Representation (ICLR), 2025.
Augustus Odena, Christopher Olah, and Jonathon Shlens. Conditional image synthesis with auxil- iary classifier gans. In Proc. International Conference Machine Learning (ICML), pp. 2642- 2017.
Kazusato Oko, Licong Lin, Yuhang Cai, and Song Mei. A statistical theory of contrastive pre- training and multimodal generative ai. arXiv preprint arXiv:2501.0466 2025.
Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predic- 2018.
tive coding. arXiv preprint arXiv:
Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhom, Jonas Müller, Joe Penna, and Robin Rombach. SDXL: Improving latent diffusion models for high-resolution image synthesis. In Proc. International Conference Learning Representation (ICLR), 2024.
Adam Polyak, Amit Zohar, Andrew Brown, Andros Tjandra, Animesh Sinha, Ann Lee, Apoorv Vyas, Bowen Shi, Chih Yao Ma, Ching- Yao Chuang, et al. Movie gen: A cast media founda- tion models. arXiv preprint arXiv:2410.13722 2024.
Rafacl Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly reward model, In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2023.
Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text- conditional image generation with clip latents. arXiv preprint 2rX1122204.06125. 2022.
Scott Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee. Generative adversarial text to image synthesis. Proc. International Conference on Machine Learning (ICMI., 2016.
14

---

Published as a conference paper at ICLR 2026
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- resolution image synthesis with latent diffusion models. Proc. IEEE/CVF Conference on Com- puter Vision and Pattern Recognition (CVPR), pp. 10684-10695, 2022.
Olga Russakovsky, Jia Deng. Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang. Andrej Karpathy, Aditya Khosla, Michael Bernstein, al. Imagenet large scale visual recognition challenge. International journal of computer vision, 1 115:211 12:22, 2015.
Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. In Proc. Advances in Neural Information Processing Systems (NeurIPS), pp. 36479-36494, 2022.
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training GANs. In Proc. Advances in Neural Information Processing Systems (NeurIPS), volume 29, 2016.
Axel Sauer, Katja Schwarz, and Andreas Geiger. Stylegan-xl: Scaling stylegan to large diverse datasets. In ACM SIGGRAPH 2022 conference proceedings, pp. 1-10, 2022.
Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. Stylegan-t: Unlocking the power of gans for fast large-scale text-to-image synthesis. In Proc. International Conference Machine Learning (ICML), 2023.
Axel Sauer, Dominik Lorenz, Andreas Blattmann, and Robin Rombach. Adversarial diffusion dis- tillation. In Proc. European Conference on Computer Vision (ECCV), pp. 87-103, 2024.
Rui Shu, Hung Bui, and Stefano Ermon. AC-GAN learns biased distribution. In NIPS Workshop on Bayesian Deep Learning, 2017.
Samarth Sinha, Anirudh Goyal, Colin Raffel, and Augustus Odena. Top-k training of GANs: Im- proving generators by making critics less critical. In Proc. Advances in Neural Information Pro- cessing Systems (NeurIPS), 2020.
Yuhta Takida, Masaaki Imaizumi, Takashi Shibuya, Chich-Hsin Lai, Toshimitsu Uesaka, Naoki Murata, and Yuki Mitsufuji. San: Inducing metrizability of gan with discriminative normalized linear layer. In Proc. International Conference on Learning Representation (ICLR), 2024.
Ming Tao, Bing-Kur Kun Bao, Hao Tang, and Changsheng Xu. GALIP: Generative adversarial clips for text-to-image synthesis. Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 14214-14223 2023.
Hung-Yo Yu Tseng, Lu Jiang, Ce Liu, Ming- Hsuan Yang, and Weilong Yang. Regularizing generative adversarial networks under limited data. In Proc. IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), 2021.
C. Wah, S. Branson, P. Welinder, P. Perona, and S. Belongie. The caltech-ucsd birds-200-2011 dataset. Technical Report CNS-TR 2000000, California Institute Technology, 2011.
Team Wan, Ang Wang, Baole Ai, Bin Wen, Chaojie Mao, Chen-Wei Xie, Di Chen, Feiwu Yu, Haiming Zhao, Jianxiao Yang, et al. Wan: Open and advanced large-scale video generative models. arXiv preprint arXiv:2503.20314 2025.
Zhuoyi Yang. Jiayan Teng, Wendi Zheng, Ming Ding, Shiyu Huang, Jiazheng Xu, Yuanming Yang. Wenyi Hong, Xiaohan Zhang, Guanyu Feng, et al. Cogvideox: Text-to-video diffusion mod- els with an expert transformer. Proc. International Conference on Learning Representation (ICLR), 2025.
Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang. Xiaogang Wang, Xiaolei Huang, and Dim- itris N Metaxas. StackGAN: Text to photo-realistic image synthesis with stacked generative ad- versarial networks. In Proc. IEEE International Conference on Computer Vision (ICCV), pp- 5907-5915, 2017.
15

---

Published as a conference paper at ICLR 2026
Han Zhang, Zizhao Zhang, Augustus Odena, and Honglak Lee. Consistency regularization for generative adversarial networks. In Proc. International Conference on Learning Representation (ICLR), 2020.
Yifei Zhang. Mengfei Xia, Yujun Shen, Jiapeng Zhu, Ceyuan Yang, Kecheng Zheng, Lianghua Huang, Yu Liu, and Fan Cheng. Exploring guided sampling of conditional gans. In Proc. Euro- pean Conference on Computer Vision (ECCV), 2024.
Yuhui Zhang, Yuichiro Wada, Hiroki Waida, Kaito Goto, Yusaku Hino, and Takafumi Kanamori. Deep clustering with a constraint for topological invariance based on symmetric infonce. Neural computation, 35(7):1288-1333) 1339, 2023.
Shengyu Zhao, Zhijian Liu, Ji Lin, Jun-Yan Zhu, and Song Han. Differentiable augmentation for data-efficient gan training. In Proc. Advances in Neural Information Processing Systems (NeurIPS), 2020.
Zhengli Zhao, Sameer Singh, Honglak Lee, Zizhao Zhang, Augustus Odena, and Han Zhang, Im- proved consistency regularization for gans. In Proc. AAAI Conference on Artificial Intelligence (AAAI), 2021.
16

---

Published as a conference paper at ICLR 2026
A RELATED WORKS
The first (class-) Joandiiacon GAN was introduced by Mirza & Osindero (2014), who incorporated class information by concatenating the input with the corresponding class embedding. This straight- forward approach has been widely adopted in subsequent works (Reed et al., 2016: Zhang et al.) 2017 Tao et al. 2023] Kang et al., 2023b). For conditional discriminators, it has been shown to be more effective to concatenate class information with intermediate discriminator features rather than directly with the input (Reed et al. (006)) a strategy now used in several modern text-to-image
GANs Tao et al. 2023 Kang et al.) (023b))
The projection-base approach, introduced by Miyato & Koyama (PD-GAN; 2018), has proven effective for both generation quality and conditional alignment, despite its simplicity. Like the concatenation-ban based approach, it requires only minor modifications to the discriminator's 's final pro- jection layer and no further architectural changes, facilitating scalability and extensibility. While the concatenation method is similar to the projection-based approach-especiinn est discriminator teatures-the projection-based method has been empirically shown to be more effective in class-conditional settings due to its well-designed inductive bias based on probabilistic modeling. This approach is now widely used in conditional generation tasks (Brock et 2019
when using the deep-
Karras et al. 2019; 2020b; [02TT] [Suuer et al.) 2022; 2023 Huang et al.) (0024) and has been ex-
tended to more challenging scenarios, such as text-to-image generation (Sauer et al. 2023 where
the set of possible text prompts is not finite.
As a more explicit approach to enforcing conditional alignment, Odena et al. (211)) proposed the auxiliary classifier GAN (AC-GAN), which adds a classifier to the discriminator to predict class labels of generated images. AC-GAN combines the standard GAN loss with a cross-entropy classi- fication loss. However, AC-GANs have been observed to suffer from limited diversity in generated samples (Shu et al., 2017). a limitation attributed to the absence of a negative conditional entropy term in the objective (Shu et al.
2017: Gong et al. 2019). Later works addressed this by applying the classification loss to both real and generated samples (Giong et al. 2019 Hou et al, 2022). Kang et al. (2021) identified instability in AC-GAN training due unbounded discriminator features and poor carly-stage classification, and proposed ReACGAN to address these issues. Separately, Kang
& Park (020) introduced ContraGAN, which incorporates data-to-data relations in addition to data-
to-class relations (Equation 4..
As shown in our experiments (Section 6.1 and recent benchmarks (Kang et al. 2023a), ReACGAN achieves SoTA performance on widely used class-image datasets among conditional discrimina- tor methods, including projection- based approaches. However, to our knowledge, this approach has not been extended beyond class-conditional settings, such as text-to-image tasks, likely due to greater implementation complexity and higher computational cost compared to projection-based and concatenation- based methods. Moreover, extending Y beyond finite discrete set (e.g., to text prompts) in this approach is generally non-trivial. Specifically, the classification loss adopted in this approach is equivalent to the InfoNCE loss (Equation (4)). which considers all plausible negative labels y' ~ Pa(y') for each training sample y ~ Pa [))x). Therefore, extending Y beyond a finite dis- crete set (e.g., text prompts) in this approach is generally non-trivial. In contrast, while BT-C and BT-M losses in SONA can also be interpreted as variants of the InfoNCE loss, as discussed around Proposition
4 they use only a single negative sample x' drawn from pa(a") per training sample drawn from Pa (1 This has two main advantages: First, this loss is easily applicable to general conditioning cases, including text-to-image, because sampling a single negative sample is feasible. Second, this property of our losses greatly reduces computational complexity, as reported in Table
For text-to-image GANs, which are more challenging than canditcondii generation tasks. both concatenation-bart based and projection-based approaches have recently been adopted. [Kang et al. (2023b) and Tao et al. (2023) employed the concatenation- approach, injecting frozen CLIP- encoded text embeddings into deep discriminator features. In contrast, [Sauer et al. (2023) adopted the projection-based approach, modeling text-conditional projections by applying a learnable affine transformation to frozen CLIP text embeddings. In addition to discriminator design, these works introduced additional losses to improve text-conditional alignment. Notably, a matching loss uses negative pairs of images and text prompts as fake samples (Kang et al. 2023b Tao et 2023). anal- ogous to our loss VRT Furthermore, all three works employed a CLIP -LI--uuidacce loss, which maxi- mizes the cosine similarity between CLIP embeddings of the text condition and generated images. A
17

---

Published as a conference paper at ICLR 2026
similar technique using an ImageNet classifier applied class-conditional GANs (Sauer al.
2022
B SUPPLEMENT FOR PRELIMINARY CONCEPTS
We review three key concepts, GAN, SAN, and Bradly-Term model, which are background of our method.
B.I GAN
GAN. Goodfellow al. 2014) originally formulated GANs two-player game between gen- erator and a discriminator. The generator aims to produce realistic samples that can fool the discrim- inator, while the discriminator seeks distinguish real samples from the data distribution and fake samples generated by the generator, outputting scalar value. Based on this framework, two variants of GAN minimax objectives were proposed. The first, known as the saturating GAN objective, is defined as:
YONI-GGANJ) = Ep (og() + (
(14)
Js GAN()) (x) (log(])) o((x))))
(15)
The second variant, referred to as the non-saturating GAN objective, shares the same maximization objective but uses a different minimization objective:
JNS-GAN (g) = - Ey,, (m) [og({(((=)))]
(16)
is well established that the global minimum of Is and INS, when ff maximizes VoRIa, is achieved if and only if Pa Pdata
The maximization objective can be equivalently rewritten as: VoRG-GAN(f)- Bpom(t) (lo[((((())))]])))))))()(()))))) ( (ogo://(())))tttppoooooooooo1110
(17)
Eppn(t) [og(r(((=))) (,,,t))log((((((((())
(18)
which consists solely of log a-) terms. We use this maximization objective for VSAN, which is applied to our unconditional discrimination.
Relativistic GAN. Selicoeu--aattines (2018) introduced relativistic variant of GANs, also for- mulated as minimax problem but based on relativistic discriminator. The original relativistic GAN, now known as relativistic pairing GAN (RpGAN), is defined using LogSigmoid as:
VIS-RIGAN(() = (ran( [lo ooooooloffaa (f(za) f(x,))
(19)
JES-RPGAN (g) (ma)e log (f((x) f(x)))
(20)
Our BT-C loss, VBT-C, can be interpreted as a conditional counterpart to Equation (9). Accordingly, we define our minimization loss for conditional alignment, JBT-C. as the conditional counterpart to
Equation 20
B.2 FROM SLICED WASSERSTEIN TO SAN
Sliced Wasserstein. Sliced Wasserstein (SW) was introduced variant of the Wasserstein dis- tance and has been further developed, resulting in important extensions such as generalized SW (GSW) (Kolouri et al., 2019) and augmented SW (ASW) (Chen et al. 2022). SW leverages key property of the Wasserstein distance: it admits a closed-form solution when the data space is one- dimensional. The closed-form expression for the Wasserstein distance between one-dimensional distributions with measures and v is given by
W Wp(, = (L, (1115"1))-=51601
(21)
where F-1(-) denotes the quantile function of the probability measure μ. The main idea of SW to exploit this closed-form by projecting digher-dimensional probability distributions onto one- dimensional spaces using the Radon transform over set of directions, defined as
RI( / T(x))((E (x, dx,,
(22)
18

---

Published as a conference paper at ICLR 2026
where the nigher-dimensionee space is projected onto one-dimensional space with direction w gD-1 Specifically, SW is defined as
D)) -VoEgo.. Rly 1/p
(23)
This decomposition of the tigher-dimensional space into collection of one-dimensional spaces makes SW much more computationally tractable than the original Wasserstein distance.
Variants of SW. Kolouri al. (2019) introduced the generalized sliced Wasserstein (GSW) distance by extending the standard Radon transform to the generalized Radon transform (GRT), defined as
GI w) - / (())((5 w)),
(24)
where g is a defining function that satisfies certain conditions (H1-H4 in Kolouri et al. (2019). The GRT includes the standard Radon transform special case. By replacing the Radon transform in the definition of SW with the GRT, the GSW is formulated as
u = (
1/2
(25)
This formulation is simple and enables a broad class of transformations for projecting data samples onto mic-dimesiional spaces. Building on this generalization, [Chnn et al.) (2022) proposed the aug- mented sliced Wasserstein (ASW) distance. The ASW is also based extension of the Radon transform, specifically the spatial Radon transform, which is defined as
T"T(E,W) = f T(x))((5 - (we, (xx))
(26)
where h is any injective function. The ASW is then defined as
(P,
WD(S In(,,), (t),
(27)
Although ASW is valid distance for distributions, it, well SW and GSW, requires dense sampling of ws on the high-ddmensiooal hypersphere for accurate approximation. To address this computational complexity, the maximum sliced Wasserstein (max-SW) distance was proposed. For example, max-ASW defined by selecting single direction that best distinguishes the target prob- ability distributions in the projected one-dimensional space, rather than integrating over all possible directions:
max-ASW" (1, max W, (()s)) (I(,,)) WESD-1
(28)
ASW is guaranteed to be distance long the function h is injective.
SAN. Takida et al. (2024) formulated SANs by modifying the discriminator optimization both the architecture and objective function. The core idea is to design the discriminator to approximately evaluate the max maX-ASW with only minor modifications. To bridge the gap between GAN optimiza- tion and max- max-ASW evaluation, they propose imposing three key conditions
the discriminator f(z) = (w, h(x)): (i) direction optimality for w, (ii) injectivity for h, and (iii) separability for h. Direction optimality motivated by the selection of a single direction in Equation (28), while in- jectivity is necessary to ensure that the discriminator defines a valid distance. detailed explanation of the third condition, separability, is provided in Appendix E.1
B.3 BRADLEY-TERRY FRAMEWORK
The Bradley-Tery framework (Bradley & Terry 1952) provides a general method for assigning scores of items based pairwise comparisons. Since its introduction. it has been widely ap- plied to various machine learning problems, particularly in reward modeling using human preference annotations.
19

---

Published as a conference paper at ICLR 2026
The core idea is model the log-odds that item zw is preferred ay the difference between their scores. Specifically, the preference scoring function, denoted as f. is learned to represent the log-odds difference between items Tw and Ze as follows:
pr is preferred over xz (b) o of y) f(xz, u)).
(29)
Hereafter, we refer to Iur and 2t as the winning and losing samples, following the convention in reinforcement learning from human feedback (RLHF). The function is learned by maximizing the following objective:
BBT Ez,.,, ( - [(x)))],
(30)
When preferences are conditioned on additional information y, the objective becomes
VET Ez.. me.y log o (f(xw. y) - f(ze.
(31)
which is equivalent Equation (8)
In our setup, we use the discriminator f as the scoring function. In typical problem setups, a dataset of paired samples with preference labels is available. However, our case, such dataset is not provided in the required format. Instead, we construct pairs of winning and losing samples in two distinct ways under reasonable assumptions. First, we assume that sample randomly selected from the dataset is always preferred over generated sample. Under this assumption, the joint distribution of winning and losing samples is defined as p(zw, Te, y) = Paata (3) Paata (I ( JP (zze (y). resulting in VBT-c. Second, we assume that sample from subset of the dataset associated with given condition is always preferred over a data sample selected without regard to the condition. In this case, the joint distribution is represented p( Ie, y) VBT-M-
Piata (V) Pdaaa Frw (y) Pdau ( (xz), resulting in
20

---

Published as a conference paper at ICLR 2026
C ALGORITHM
Please refer to Algorithm for the pseudo code describing GAN training with SONA. Note that, in the application to GALIP (Section 6.2 we use frozen CLIP text embeddings to model wys which does not involve the optimization of in Algorithm
Algorithm 1 GAN Training with SONA
Input: Data distribution Pdati latent distribution pzi generator parameters 0; discriminator (w, Wy. $), where & models as his parameters for learnable weighting (SSAN, SBT-C, ŠBT-M); batch size N; learning rates (no, Mu Buys Mp. Ma); total iterations T; update ratio
parameters =
for 1 ..,,....7 do
for = 1.2..... do
Obtain weight coefficient sets by
(SSAN, (BT-M..STTMM = Normalize o Softplus SBT-C, SBT-M)
Sample minibatch [Tdammm yn) [n)]ne(N) from Pdata
Sample latent variables ( from pz
Generate synthetic samples genn, 90 9n) for [N]
Create negative samples Ineg.n = (n) using a random permutation i
Compute VSAN, VBT-C, and VBT-M with {F Wneg,ns Zgen,ns 3n) MN)NN
Update w -- w + Th V (VSAN VAT-C + VATMM)
Update N +- vi The V e (VSAN + VBT.C + VBTM)
Update á + The V (VSAN + VBT-C + VBT-M)
Update wiy wy Thi Vu, (VBT-C + VBT-M)
end for
Sample minibatch [<dmm,,, yn IEENN] from Pdata Sample latent variables [aN]NE from pz (z)
Generate synthetic samples Zgen.n = g0 Zas Fn) for n [N] Compute JSAN and JBTC with (Fraaa,, Zgen,, ne))
Update 0 + TJe V (JAAN + VBT-c)
end for
D ANALYSIS OF EXISTING APPROACHE
D.I PROPOSITION
We introduce the following lemma, which is taken from the proof of Zhang et al. 2023 Proposi-
tion 1).
Lemma 5. The function f maximizes VeE if f(x,y) log Panta (xly) + (x(x) for an arbitrary function Tx x x+R. R.
Proposition (Log conditional probability maximizes VCE). Assume Paauly) is constant re- gardless of y E Y, egg., uniform distribution. The function f maximizes VCB if f(x, v) = log Pdata (y)x) + +rx for arbitrary function rx : R.
Proof. By Lemma 5 the maximizer f can be written as
f(x, u) log Panta (xly) r'x (æ),
(32)
where r'x X + R is arbitrary function. By Bayes" theorem, have
log Pdma (xl1) log Paam (y/(z) log Pdata (x) log Pdata (v)
(33)
= log Panu (y)xx) Poggaaa (x) + C,
(34)
where C' denotes the constant log Paax(() since P3)a(y) is assumed to constant. Substituting Equation 34 into Equation (32) completes the proof.
21

---

Published as a conference paper at ICLR 2026
E ANALYSIS OF SONA
E FORMAL STATEMENT OF PROPOSITION
We formally state Proposition this section.
First, we introduce two key assumptions required for this proposition. To do so, we present the concept of separability from Takida et al. (2024), which is used to formulate assumptions on the function h in the discriminator. This property is important for ensuring that the discriminator induces a meaningful distance between target distributions.
The definition of separability relies on the spatial Radon Transform (Chen et al. 2022 SRT), defined as follows:
Definition 1. (Spatial Radon Transform) Given measurable injective function h X R and function U X + R. the spatial Radon transform of U is
S*U(,,w) = Js U(z)0(5- (w, (x))))dx,
(35)
where Ç E IR and w E SD-1 parameterize the hypersurfaces {ar E X (w, h(x)) = E}.
The SRT generalizes the Radon Transform using an injective function. I a probability density, the SRT corresponds to applying the standard Radon transform to the pushforward of U by h. In this case, intuitively, the SRT projects h(x) onto scalar along direction w with the probability. One of its crucial properties is that, for two probability densities and q, if S"p(E,w) = Sh w) is satisfied for all E E R and w E SD-1, then p = q holds due to the injectivity of h. Thus, an injective h preserves information about the equality of target distributions. This leads to our first assumption:
Assumption A. We assume that h X + RD is injective.
Using the SRT, we define separability as follows:
Definition 2. (Separable) Given probability densities p and q on X, and h X RDD let W 8D-1, and let Ex (-) denote the cumulative distribution function of w)). w = arg max Ep(aa) ((w,, h(xx))) - Bow h(x))) satisfies F/."" (g) S FR. (E) for all g E IR then h is separable for and g.
and
Intuitively, separability ensures that the optimal transport map in the mee-iimnnioonll space induced by the SRT from s""((,w"" to """(""""" is aligned the same direction for all samples. This sug- gests that h can bring p and g closer, at least along the optimal direction w", which also maximizes VsAN(w, ft) for given h. Thus, we make our second assumption:
Assumption B. We assume that h X + R.D is separable for Panta (1) and py
With these assumptions, can now formally state Proposition
Proposition 2 (Formal: Unconditional discrimination by VSAN). Let the discriminator be f(x) (we, (x(x)) with w E D- and h X + RD, Suppose Assumptions and B hold, and let w arg max_ VSAN (w, h) for a given h. Then, the objective JsAN âs, h) is minimized if and only if g minimizes the following functional mean divergence between Pana (z) and Py(x)), given by
A
FM (pdata Pa)
(z) [h(x)] Bpp(t)) [x())]]2
(36)
which is a valid distance under these assumptions.
The proof of Proposition 2 is provided in Takida al. (2024).
E.2 PROPOSITION 3
We introduce a lemma, which is restatement of portion of claims made in Theorem 3.1 of Kolicoeur-Martinee (2020).
Lemma 6. Let R R. be a concave function such that v(0) C. is differentiable O, o0) # O, sup,(u(t) > O, and arg (u())) > 0. Let and q be probability distributions with support X. Then, sup, ((((() [(x') is divergence, up to C.
22

---

Published as a conference paper at ICLR 2026
Proposition (Conditional learning by VBT-c). Let the discriminator be f(r, y) (x)
f (z, y). where f (z) = (w. h(z)) with w E SD-1, 1 X RR. b R. and f X XY R. Assume that the generator achieves (x( Pdaa(a),, and and h maximize VSAN for given Pdata and Pg. If f maximizes Equation 13 then it is minimized if and only if Pdata (xla())y))))))))))))){())) Pg (z for y E Y.
LAT.C Epan(y))ur (ew (w..) (wwl) ( + (A (
( - (xe, v))l
Proof. Given Pa(x) = Paata (2) and the optimality of f for the specified Py and Pdata- it follows that (x)x)) = C for x E X, where C constant. Substituting this into Equation ( we
obtain:
CBT-c(wy..)) = Pana Iy),, (ze log Dogo(((C) (zw, (C ff (x2.
pu (a (x)
log a (5 ( - (
(37)
Since log a()) satisfies the conditions of Lemma 6 applying this lemma to Vure and Var-c estab- lishes the claim.
Note the assumption of distribution matching. In Proposition 3] we assume (a( (r) for theoretical develop- ment, which we acknowledge is a rather strong condition. We empirically verify that the effectiveness of the conditional alignment term SONA does not de- pend on this assumption being satisfied in practice. demonstrate this, we plot the FID score and Top-1 accuracy with respect to training steps for ImageNet (batch size 2048) in Section 6.. This figure shows that conditional alignment improves from the beginning, even when there is still a deviation between (x) and Paata (1) in terms of FID, as observed ReACGAN and PD-GAN.
10
0.6
FID FID-50m SONA
PD-GAN
Top1 SONA
ReNCGAN
Tepl
101
0.1
0
25
50
75
100
125
150
175
200
Training step / 10
Figure B: FID (L, an indicator of generation perfor- mance) and Top-1 accuracy (t, an indicator of condi- tional alignment) function of training iteration.
E.3 PROPOSITION 4
We introduce a lemma (presented in the proof of Oko et al. (2025 Lemma 1) in the discrete case), which will come in handy for the proof of Proposition 4
Lemma 7. Consider minimizing VIntONCE over all possible functions f f: X x +
exp(f(x,)) y))
VInfONCE()) = Epan (psa((..)))m log exp( (a, v)) + ex (z'.
(38)
VInoNCE is maximized if f(x,y) = (ogPamaaylz)) + (y) for arbitrary function TY Y Y + R.
Proof. This proof is essentially
a modification of the proof of Oko et al. 2025
Lemma 1) to our
case. Let a and of zf..z be probability mass functions over {0, 1} given by
Pdsta (o V)Paata (x11
Pdata (3) 2r)
qma.m an. (0) Pdata (Io, y) Paata (x1) + Pdota (I1, y Paita (2o)
Pdata (20) + Pdttaa (1) (
and
cxp(f(x0:1)
d 2n exp(f(xo, w)) + exp(f(x1,,))
23

---

Published as a conference paper at ICLR 2026
Then, have
1 VintONC: (J) = 7 (Pa (Ro.)) [lg / 21..21.9 (0)) + Paa (21 (ppaa Dog v 220. (1)])
F * (Fo (xm) (M)m (1 (0) log zf.. (0) lo w (1) log oo (1)
(o) m1.0 o m.)l
where Hig, oz) B log / is the cross entropy, which is minimized when q' q. Since of holds when f fax v) log Paita (y/z) + ry (v) for a function ry, we have proven the assertion.
Proposition (Log gap probability maximizes VBT-x). The function f maximizes VBT-M if f(x, 4)
log Pdata y) log Pdarn (Ir) + (y) for an arbitrary functtio TY Y ++
Proof. The objective VBT is reformulated
VFT-M(f) = Epan (y))aa @ Wirum (n) [f f(xx, v))l
(39)
exp(f(xw.)) v))
Epau (a (P)aaa)) log exp(f(x y)) + exp(f(xt, B))
(40)
Therefore, the claim has been proven as a direct consequence of Lemma 7 and Bayes' theorem: log Panaayl(r)) log ( y)) log Pdata (r) +
Equation 440) is now equivalent to VInLNNEE
log JugPaaaa (v).
Note that, from the proof of Lemma can also prove the "only if" statement up some Puata Puatt-Null -uull sets.
E.4 INSIGHT INTO ADAPTIVE WEIGHTING
We provide insight into the adaptivity of our proposed weighting scheme, which employs learnable scalar parameters SAAN SÆT... and 2 ST-M- by simplifying the maximization objectives.
Recall that the maximization objectives VSAN. VBT-C. and VETM can be expressed with log (LogSigmoid) imiid) in the following form:
V = Pppaa(iip(ss)))(a"l))) [lo
((]((x) (lgoo (x)))(((')))
(41)
Specifically, VeT-c is recovered by setting fi f2 = f. Pdnta (-1y), and Py(-ly) in Equa- tion 41). while VET- is obtained by setting fı = f2 f.P Paasa (-1v), and q Pdata
Recall also that we adopt VORIG-GAN proposed in Goodffelow et al. (2014) (see Equation Appendix B.T) define VSAN. which specifically formulated as:
18 in
VSAN = Epen(e) [log af ( (x)) + ppp [log a (- (x))
(42)
= (x) [log af (us, h(x)) - b))] + Ep, llg a (w, M())))
(43)
where VSAN includes two terms involving log (-), each recovered by setting (p, f2) (pdatas Pdotas (w, h), b)) and (p.q. f2) (p Pa. b, (w, h1) in Equation (41), respectively.
As proposed in Section 4.4 we replace log (1) with log a(s 1)/s i in Equation (41) yielding:
log a (s(f (
Vss. (w
(44)
For simplicity, we consider a single update step for and a one-sample approximation of the expec- tation (for VORIG-GAN, we stochastically compute either the first or second term Equation (43 per iteration). This leads to:
Lis (s( fz((')),
(45)
Af
24

---

Published as a conference paper at ICLR 2026
where z and x' q. The derivative of VLS,. with respect to is:
ahs,,
0
[
log (s
(46)
Ōs
Os
1
sAi
log (s
(47)
s
exp(sAff +1
For 0 < (from the constraint on s), this derivative oVL.../Os has the following properties:
(PI) For fixed 0 < < 1 and any Af. it is monotonically increasing with respect to Af.
(P2) For fixed Af 2 it is monotonically decreasing with respect 8.
To illustrate these properties, consider the two-term case:
log (s1 + log logo
(48)
$1
$2
In this setup, (P1) implies that when 0 < 81 52 1, the coefficient corresponding to the larger error between Af1 and Afz yields larger gradient, meaning the larger error is prioritized by increasing its coefficient.
(P2) implies that when Afi Af2 0, the smaller of $1 and s2 has larger gradient, leading to $2 if this equality persists during optimization.
Kendall et al. (2018) proposed an adaptive weighting scheme that introduces a scalar parameter to represent uncertainty. Although this method shares some similarities with ours, their method balances multiple terms using (learnable) unbounded coefficients, which can diverge as training progresses. This unbounded growth is undesirable in our case, as GAN training stability is generally sensitive to the learning rate.
F EXPERIMENTAL DETAILS
F.1 MoG EXPERIMENTS SECTION 5.2
We empirically evaluate proposed method in two-dimensional space X R... The target mixture of Gaussians (MoG) in X consists of N isotropic Gaussian components, each with variance 0.03² and means evenly distributed on circle of radius 0.75. The generator is modeled with 10-dimensional latent space 2, where the base distribution p(z) is standard normal.
Both the generator and diseriminator use simple fully connected (FC) architectures, following pre- vious work (Mescheder et al., 2017] Nagarajan & Kolter 2017: Sinha et al. [2020] Takida et al.) 2024. Specifically, each network consists of three hidden FC layers with 50 units per layer. The generator uses ReLU activations, while the discriminator uses Leaky ReLU, which facilitates the discriminator's 's injectivity (Takida et al.) (024). The last linear layer in the discriminator corre- sponds and w: for SONA and PD-GAN, respectively. For class conditioning in the generator, we use four-dimensional learnable class embeddings concatenated with the input noise z. For discriminator, we use additional class-dependent embeddings: wy for PD GA-GAN and wy for SONA. In SONA, both the linear projection and the embeddings in the discriminator are normalized to ensure w., wy 1
For training, we use a batch size of 256 and the Adam optimizer (Kingma & Ba 2015) with (81, 82) (0.0, 0.9) and learning rates of 0.0001 for both the generator and discriminator, The update ratio is set to 1, meaning the discriminator is updated once per iteration. Models are trained for 15,000 iterations, and the checkpoint with the lowest w2 value is selected the best model.
Wasserstein-2 distances for W2, cW2, and NF are computed using the POT toolbox Flamary et al. 2021 2024) with 10,000 samples per distribution.
https:://gittuub.com//ttttt
25

---

Published as a conference paper at ICLR 2026
Figure 5: CIFARIO: (Left) Generated samples by SONA with BigGAN, (Right) Generated samples by SONA with StyleGAN-2.
F.2 CLASS CONDITIONAL GENERATION TASKS IN SECTION 6.1
F.2.1 EXPERIMENTAL SETUP
We base our experiments on the benchmarking repository provided by ByTorch-StudioGAN (Kang et 2003aa. For hyperparameters such as learning rate and batch size, we strictly follow the default configuration provided PD-GAN.
To ensure fair comparisons, we conduct all experiments ourselves and report the resulting scores in the tables. All models are trained on CIFARIO 10 and TinylmageNer three times with different random seeds; we report the mean and standard deviation of the scores in Tables and For ImageNet, due to the high computational cost (each training run requires 8 and 40 H100-days for batch sizes 256 and 2048, respectively), we report results from a single run.
For baselines, we select two representative classifier-based methods, ContraGAN and ACGAN, and projection-based method, PD-GAN. Since primary objective is compare SONA with other state-of the-art discriminator conditioning methods, we not include additional data aug- mentation (Karras al., 2020a Zhao et al. 2020) discriminator regularization techniques (Zhang) et al., 2020 Zhao et al. 2021 T'seng et al. 2021), as these are orthogonal to our approach. To demonstrate that our method can be combined with such techniques, we also compare SONA and the baselines using the Diff'Aug data augmentation method (Zhao et al. 2020), and confirm that the performance of SONA can be further improved, as shown in Table
F.3 TEXT-TO-IMAGE GENERATION TASKS IN SECTION 6.2
F.3.1
EXPERIMENTAL SETUP
We base our experiments the benchmarking repository provided by Kang al. (003a)). For hyperparameters such as learning rate and batch size, we strictly follow the default configuration.
F.3.2 CONVERTING GALIP DISCRIMINATOR WITH SONA
Discriminator architecture. We briefly review the discriminator architecture proposed by Tao al. (2023), which serves as base architecture. The GALIP discriminator consists of frozen CLIP-VI ViT and a learnable module called Mate-D. -D. Mate-D is designed to effectively utilize deep fea- tures extracted from both images and text using CLIP. Specifically, Mate-D comprises CLIP Fea- ture Extractor (CLIP-FE) and a quality assessor (QA). The CLIP-FE aggregates multi-layer features from CLIP-VIT using a sequence of extraction blocks, each containing convolutional and ReLU
26

---

Published as a conference paper at ICLR 2026
Figure 6: TinylmageNet: Generated samples by SONA applied with DiffAug.
Figure 7: ImageNet: Generated samples by SONA trained with batch size of 2048.
layers, to progressively refine visual representations. The final extracted features are concatenated with replicated sentence vectors obtained by feeding text prompts (y) into the CL.P text encoder. These concatenated features are then evaluated by the QA, which predicts conditional likelihood using additional shallow convolutional layers assess image quality. The dimensionality of the final extracted features, corresponding to h(x)) in our formulation, and the sentence vector, denoted e(y), are 512 and 512 x respectively. The QA converts e(y) 1R512 E(y) |512x7x7 by replicating the 512-dimensional vector 49 times to enable concatenation.
Applying SONA this discriminator requires only modifications the QA. We add single train- able 512 x 7 x 7-dimensional parameter to model w. For Wy, we directly use the extended text embeddings Fly). Notably, even though Wy is frozen in this setup, SONA achieves improved generation performance and comparable text alignment. We also experimented with modeling wy using learnable modules, such as a learnable affine layer or shallow FC network applied to e(y) to produce 512 7 7-dimensional feature. However, these approaches degraded performance, par- ticularly in text alignment. We suspect that applying such learnable operators to CLIP features may cause information loss and prevent full utilization of the pre-trained representations without careful design. Designing suitable modules for w, based on CLIP features remains an open direction for future work.
27

---

Published as a conference paper at ICLR 2026
sandl bright we tee birt ootn prey heed while strped
birt stiped back thae grey, brand
this
almoet wiecctive
adned hind oroened
birt haw sgrey belly, with browm
lonsew cleck.
fee sarsame a thin and
speachedd los ayard
back wings
with matur "eather,, brack
atrapht
ong
oney pray sing
and intellgent
apot the bresal.
and lcck at the up
and tall foult ons.
and gree mod
Figure 8: CUB: Generated samples by SONA.
Agraite walking around yard near farcs.
beach with poogle nalaaing on some
mann beo shatsbour doon skbewalk nead
ba stalion with poople we buig around
Awale toppod with banareo
The ludky boka the gaing
costare poue for photo
on srow covered holding
Figure 9: COCO: Generated samples by SONA.
Training objective. GALIP incorporates additional objective terms and techniques into both the discriminator and generator losses enhance text alignment.
For the discriminator, the fake distribution (i.e., the generator distribution in standard GANs) is aug- mented with a mixture distribution that combines the generator distribution and a mismatched data distribution, formed by incorrect image-text pairs in equal proportion. To further stabilize adver- sarial training, a matching-awer aware gradient penalty (MAGP) applied both the extracted CLIP features and their corresponding text features. For the generator, CLIP-based cosine similarity loss added encourage both image quality and text alignment. The overall objective functions are given by
VGALIP(f) = (paal [min(0,, -1 f(xa. u)) + 2 po [min(0, -1 (mii)))mmm( f(Igz v))l
(49)
E (sa) (min(0, -1 f(xa, v))l ) MAGP
(50)
JGALIP(g) -F,, py) (v) [ (2rg u)] >z R, (Fg (VPaa(())) (c))
(51)
where SCLIP denotes the CLIP-based cosine similarity.
For fair comparison, we partially follow the original loss by adding MAGP to the discriminator loss and including the same Cl.ed-based similarity loss in the generator objective. For the remaining loss terms, SONA provides direct counterparts, which replace the original objectives. We use exactly the same values of Y and X2.
G GENERATED SAMPLES
Generated samples by SONA trained in Section can found in Figures
10
H LIMITATIONS AND FUTURE WORKS
Method. Our method is, in principle, applicable to wide range of conditional generation tasks. However, efficiently modeling conditional projections wy still challenging when Y not a finite discrete set (e.g., when Y consists of plausible text captions or is continuous). In our text-to-image experiments (Section 6.2). we use frozen embeddings from a pre-trained CLIP encoder, which may limit the discriminator's representational power for conditional alignment. Developing effective approaches for modeling conditional projections that generalize to arbitrary types Y remains an open problem.
28

---

Published as a conference paper at ICLR 2026
picture Agii playing
soliary Japar lemplle, Japar
sege yord.
biggele
sulemwegeed enggino
light
Paviitio.
Figure 10: GALIP models trained on CC12M: (Top) Generated samples by GALIP (concat). (Bot- tom) Generated samples by GALIP with SONA. Text prompts are from the COCO dataset.
In Proposition we assume the discriminator is globally optimal. While this assumption common in the literature (Goodfellw al. 2014 Johnson & Zhang 2019] Gao al. 2019 Fan al. 2022 Li al. 2018 Chu et al. 2020), it rarely holds in practical GAN optimization. Extending the theoretical analysis to more relaxed and realistic conditions on the discriminator an important direction for future work.
Theoretical Analysis.
Experiments. We evaluated our approach on standard benchmarks with images up to 256 resolution, addressing both class- and lext-conditional generation tasks. Expanding to wider range of conditioning modalities (e.g., segmentation maps. image style) and larger-scale settings (c.g., 512x512 or higher, progressive learning setups (Sauer et al.) 2022), ), as well as extending beyond image generation to domains such as video and audio generation, are important directions for future research.
Future Works beyond GANs. Our scope is discriminators, which are beneficial general genera- tive models beyond GANs, including diffusion models. One of the most active areas in this line is diffusion distillation into one-step or few-step generative models. Adversarial Diffusion Distillation (Sauer et al. 2024] ADD) a pioneering paper of this direction, in which adversarial loss based on discriminator is used altogether with the usual distillation loss, enhancing the distillation perfor- mance significantly. ADD is backbone framework used for training SDXL Turbo, well-known high-quality text-to-image model. Besides ADD, some work also employs adversarial training to enable the generation of high-quality samples with one step (Kang et al.) 2024 Lin et al. 2025) Chen al.) 2025a). According to this literature, improving discriminators can potentially lead to improved diffusion-based generative models. While it is an interesting trial to apply SONA to such distillation methods, represents a substantial topic for future investigation.
29


Reviews:
[{"review_id": "cBM03dGYQ0", "reviewer": "Reviewer_ip5t", "summary": "The paper proposes SONA, a conditional GAN discriminator that focuses on these two objectives (a) unconditional “naturalness” scoring from (b) conditional alignment via orthogonal projections, and augments training with mismatching-aware supervision and adaptive weighting across objectives. \nThe unconditional term is trained with a slicing adversarial networks (SAN) objective, while alignment uses two Bradley–Terry pairwise losses—one for conditional discrimination and one for mismatch awareness—plus a light adaptive weighting to keep the objectives balanced.\nThe method’s overall loss learns data realism and condition faithfulness without the two interfering. Empirically, SONA improves FID/IS across CIFAR-10, TinyImageNet, and ImageNet-128; it also plugs into a text-to-image GAN (GALIP) and gets consistent FID gains The paper includes propositions analyzing the objectives and ablations supporting the design choices.", "questions": "should there be :\n\nConsistent usage of matching-aware vs mismatching-aware throughout the paper. In Abstract (and consistently across the paper): “matching-aware (supervision/discrimination)” → “mismatching-aware …” (to match the title and the negative-pair supervision described).", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The proposal of “sum of naturalness + alignment” with an explicit orthogonal projection is a nice inductive bias and factorization that reduces interference between realism and conditioning by construction in the objective function.\n- The paper shows consistent improvement across standard cGAN settings, including a nice ImageNet-128 table and a clean plug-in to GALIP for text-to-image.\n- The paper shows the ablation experiments that separates out the impact of the orthogonal split, mismatch-aware loss, and adaptive weights.\n- The source code is attached in the supplementary for reproducibility.", "weaknesses": "- The experimental comparisons emphasize AC-GAN-style and projection GANs; some more discussion on strong GAN baselines and competitive diffusion/rectified-flow generators could help strengthen the empirical case, especially on ImageNet.\n- The paper introduces additional pairwise losses and learnable weighting under a normalization constraint, maybe some discussion on the compute/memory overhead could help readers evaluate the efficacy of the proposed approach reproduce gains reliably.\n- For GALIP, ω_y is frozen from CLIP and the CLIP-score improvement seems kind of incremental. It could help the readers if larger-scale text-to-image (higher res, varied prompts) and a learnable ω_y variant experiment could be performed to check the alignment benefits in richer/diverse settings.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Wjp07hhGc2", "reviewer": "Reviewer_cYPq", "summary": "This paper proposes SONA, a novel discriminator design for conditional Generative Adversarial Networks (GANs). It addresses the core challenge of balancing sample authenticity (naturalness) and conditional alignment by decomposing the discriminator's role into three integrated capabilities: robust unconditional discrimination, enhanced sensitivity to conditional alignment via negative samples, and dynamic adaptive weighting of these objectives. The method employs separate, orthogonal projections for naturalness and alignment, supported by a combination of Slicing Adversarial Network (SAN) and Bradley-Terry (BT) model-based losses. Extensive experiments on class-conditional (CIFAR-10, TinyImageNet, ImageNet) and text-to-image generation tasks demonstrate that SONA outperforms state-of-the-art methods in both sample quality and conditional alignment.", "questions": "The paper shows that using a learnable ω_y for text conditioning degraded performance. Could the authors speculate more on the reasons for this? For instance, does the frozen CLIP embedding provide a more stable and semantically meaningful direction that is difficult to improve upon with a simple learned transformation? Have the authors explored more complex parameterizations (e.g., small MLPs) for ω_y?\n\nProposition 3 assumes p_g(x) = p_d(x). In practice, how sensitive is the effectiveness of the conditional alignment term V_BT-c to deviations from this perfect unconditional matching? Are there empirical observations from the experiments (e.g., from the MoG study) that suggest the conditional alignment learning remains effective even when unconditional FID is still being optimized?\n\nThe adaptive weighting mechanism is a simple solution. Did the authors experiment with or consider other adaptive weighting schemes from multi-task learning (e.g., based on uncertainty or task homoscedasticity) and, if so, how did they compare to the proposed method?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "+ This paper proposes a novel discriminator architecture that explicitly decouples sample naturalness learning and conditional alignment through orthogonal projection. The combination of SAN and BT model objectives is innovative.\n\n+ The paper is clearly written, explaining the proposed concepts in a simple and understandable way. The structure is logically rigorous, and the diagrams effectively complement the textual explanations.\n\n+ The method validates its improvements in both standard and challenging benchmarks, and its applicability in text-to-image generation highlights its broad application potential.", "weaknesses": "- Lacks comparison with a simple dual-projection design, failing to demonstrate the necessity of the orthogonal constraint and potentially adding unnecessary complexity.\n- Training speed is consistently slower than the simplest baseline (PD-GAN), without discussion of whether the performance gain justifies this overhead.\n- The core theory relies on the strong, often unrealistic assumption of \"perfect distribution matching,\" with no discussion of its validity in real-world training.\n- The absence of a direct comparison with contemporary hybrid discriminators like ADC-GAN, which also integrate unconditional and conditional discrimination, makes it difficult to fully assess the innovative advantages.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yk46hHOjHF", "reviewer": "Reviewer_xeHQ", "summary": "The paper addresses a key limitation in conditional GANs, which often struggle to jointly ensure image authenticity and alignment with conditioning inputs. To mitigate this, they propose SONA, a novel discriminator architecture that integrates unconditional discrimination, matching-aware supervision, and adaptive weighting. Experiments on class-conditional and text-to-image generation tasks demonstrate that SONA achieves superior sample quality and conditional alignment compared to existing methods.", "questions": "Mentioned in the weakness section.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The paper includes comprehensive experiments conducted across diverse datasets and scales, supporting the generality of the proposed method.\n* The paper includes an ablation study that justifies the contribution of each model component. It would be helpful to include visualizations to show how each component affects output quality.\n* The writing is clear and well-organized.", "weaknesses": "* The relevance of the addressed problem is uncertain in the current context, where most major advances in generative modeling stem from diffusion models rather than GANs. Moreover, the compared baselines are relatively outdated GAN architectures, making the reported improvements less meaningful. It remains unclear whether the proposed approach would offer advantages over using state-of-the-art diffusion-based methods, which limits the overall impact of the work.\n* The paper lacks baseline comparisons with modern diffusion models, which currently outperform GANs on most conditional generation benchmarks.\n* Missing qualitative results. Given that the task involves image generation, it should include visual comparisons illustrating how the proposed method improves sample quality and conditional alignment relative to existing approaches.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "O4jsToIis7", "reviewer": "Reviewer_nbxK", "summary": "This paper introduces SONA (Sum of Naturalness and Alignment), a new discriminator framework for conditional generative adversarial networks (GANs). The motivation stems from a persistent issue in conditional generation: balancing sample authenticity (unconditional discrimination) with conditional alignment (matching the conditioning signal such as class labels or text prompts). Traditional discriminators, such as those in AC-GAN or projection-based GANs (PD-GAN), handle these two aspects in an intertwined manner, often requiring careful weighting or suffering from limited sensitivity to mismatched conditions.\n\nSONA explicitly decomposes the discriminator’s learning objective into three coordinated components:\n\n1. Unconditional discrimination, focusing on the authenticity of generated samples via the Sliced Wasserstein perspective;\n\n2. Matching-aware discrimination, improving alignment sensitivity by introducing mismatched (negative) samples through a Bradley–Terry pairwise comparison formulation;\n\n3. Adaptive weighting, dynamically balancing the above objectives through learnable coefficients constrained by normalization.\n\nThe proposed design uses orthogonal projections of discriminator features to separately assess naturalness and alignment, encoding an inductive bias that disentangles these two factors. The theoretical analysis establishes that each component corresponds to optimizing distinct divergences (e.g., log-probability gaps between conditional and unconditional distributions).\n\nEmpirically, SONA achieves consistent gains over state-of-the-art baselines (ReACGAN, ContraGAN, PD-GAN) on CIFAR10, TinyImageNet, and ImageNet, improving both FID and Inception Score across multiple backbones (BigGAN, StyleGAN2). The method further extends effectively to text-to-image generation tasks (CUB, COCO, CC12M) when integrated with GALIP, achieving better FID and comparable CLIP alignment. Ablation studies confirm that orthogonal modeling and mismatching-aware loss significantly contribute to performance improvements.\n\nOverall, SONA presents a unified, theoretically sound, and empirically validated framework for improving conditional discriminators, offering both conceptual clarity and practical robustness in modern GAN training.", "questions": "1. Computational overhead: How much additional computation or memory does SONA introduce compared to standard PD-GANs, particularly due to pairwise BT loss sampling and adaptive weighting? Is the training speed comparable?\n\n2. Stability and convergence: Theoretical results show desirable properties at equilibrium, but how stable is the actual training dynamic? Did the authors observe any oscillations or mode collapse before convergence?\n\n3. Generalizability to diffusion models: Since diffusion-based models dominate text-to-image generation, can SONA’s discriminator concept be repurposed as a “critic” for conditional diffusion or consistency models?\n\n4. Scaling to complex conditions: How does SONA perform when the conditional space is continuous or high-dimensional (e.g., embeddings or attributes rather than discrete labels)?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. Novel conceptual integration: The paper elegantly unifies multiple important discriminator desiderata—unconditional, conditional, and mismatching-aware discrimination—into one coherent framework. The separation of naturalness and alignment projections via orthogonality is an intuitively appealing and theoretically well-justified idea.\n\n2. Sound theoretical grounding: Each component of SONA is supported by propositions that connect its loss functions to meaningful probabilistic interpretations (e.g., conditional divergence minimization and log probability gap maximization). The use of the Bradley–Terry model for conditional discrimination is a clever adaptation rarely seen in GAN literature.\n\n3. Strong empirical performance: The method demonstrates clear and consistent improvements across diverse datasets and architectures. Especially on ImageNet (FID=6.14, IS=140.14), SONA substantially outperforms prior methods, showing robustness at scale. The inclusion of text-to-image benchmarks further validates its generality.\n\n4. Comprehensive experimentation: The authors conduct detailed comparisons with strong baselines (PD-GAN, ReACGAN, ContraGAN), extensive ablations (adaptive weighting, orthogonal projection, mismatch loss), and visualization using toy datasets (MoG). This provides convincing evidence of both quantitative and qualitative improvements.\n\n5. Reproducibility and transparency: The paper references open-source implementations (StudioGAN, BigGAN-PyTorch, GALIP) and commits to code release. Appendices include detailed algorithmic descriptions and theoretical proofs.\n\n6. Practical relevance: Since projection-based discriminators remain a backbone of modern GANs, SONA’s design can be easily adopted without significant architectural overhead, making it both theoretically elegant and engineering-friendly.\n\nOverall, the paper succeeds in addressing a long-standing problem (balancing authenticity and alignment) in a way that is theoretically principled, empirically validated, and broadly applicable across generative modalities.", "weaknesses": "1. Complexity of formulation: While conceptually clean, the proposed method involves multiple interrelated objectives (SAN, BT-COND, BT-MM, adaptive weighting), which may make training more cumbersome in practice. Although the authors report stability, more discussion on convergence behavior and computational overhead (especially in large-scale settings) would strengthen the paper.\n\n2. Limited comparison with diffusion-based models: The field has largely shifted toward diffusion and rectified flow architectures for conditional generation (e.g., SDXL, RF Transformers). While SONA’s GAN focus is clear, the paper could better contextualize its relevance in the broader landscape of generative modeling in 2025–2026, potentially by discussing hybrid or complementary uses.\n\n3. Ablation depth: While ablation studies isolate major components, finer-grained analysis (e.g., sensitivity of adaptive weighting parameters or orthogonality constraint strength) is missing. It would also be useful to examine cases where SONA may underperform or produce mode collapse, to better understand its limitations.\n\n4. Clarity and accessibility: The theoretical derivations, especially those involving the Sliced Wasserstein and Bradley-Terry frameworks, are mathematically dense and may be challenging for readers not familiar with those formulations. A more intuitive explanation or schematic of the optimization flow could enhance accessibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)