SPARKE: Scalable Prompt-Aware Diversity and Novelty Guidance in Diffusion Models via RKE Score
Authors: Mohammad Jalali
Haoyu LEI
Amin Gohari
Farzan Farnia
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Models
Guidance
Diversity
Kernel Entropy Measures
Primary area: deep_learning
TL;DR: SPARKE is a scalable method for prompt-aware diversity and novelty guidance in diffusion models by leveraging conditional kernel entropy, efficiently scaling to SOTA latent diffusion models.

Abstract: Diffusion models have demonstrated remarkable success in high-fidelity image synthesis and prompt-guided generative modeling. However, ensuring adequate diversity in generated samples of prompt-guided diffusion models remains a challenge, particularly when the prompts span a broad semantic spectrum and the diversity of generated data needs to be evaluated in a prompt-aware fashion across semantically similar prompts. Recent methods have introduced guidance via diversity measures to encourage more varied generations. In this work, we extend the diversity measure-based approaches by proposing the *S*calable *P*rompt-*A*ware *R*eny *K*ernel *E*ntropy Diversity Guidance (*SPARKE*) method for prompt-aware diversity guidance. SPARKE utilizes conditional entropy for diversity guidance, which dynamically conditions diversity measurement on similar prompts and enables prompt-aware diversity control. While the entropy-based guidance approach enhances prompt-aware diversity, its reliance on the matrix-based entropy scores poses computational challenges in large-scale generation settings. To address this, we focus on the special case of \textit{Conditional latent RKE Score Guidance}, reducing entropy computation and gradient-based optimization complexity from the  $\mathcal{O}(n^3)$ of general entropy measures to $\mathcal{O}(n)$. The reduced computational complexity allows for diversity-guided sampling over potentially thousands of generation rounds on different prompts. We numerically test the SPARKE method on several text-to-image diffusion models, demonstrating that the proposed method improves the prompt-aware diversity of the generated data without incurring significant computational costs. We release our code on the project page: [https://mjalali.github.io/SPARKE/](https://mjalali.github.io/SPARKE).

SPARKE: Scalable Prompt-Aware Diversity and Novelty Guidance in Diffusion Models via RKE Score
Mohammad Jalali' Haoyu Lei!* Amin Gohari Farzan Farnia'
Department of Computer Science and Engineering, The Chinese University of Hong Kong DDpartment of Information Engineering, The Chinese University of Hong Kong fmjalali24, hylei22, farnia)&cse. cuhk. hk, agohari@ie cuhk. edu. hk
Abstract
Diffusion models have demonstrated remarkable success in high-fidelity image synthesis and prompt-guides guideggiddd generative modeling, However, ensuring adequate diversity in generated samples of prompt-guided diffusion models remains chal- lenge, particularly when the prompts span broad semantic spectrum and the diversity of generated data needs to evaluated in prompt-aware fashion across semantically similar prompts. Recent methods have introduced guidance via di- versity measures to encourage more varied generations. In this work, we extend the diversity preasurebbased approaches by proposing the Scalable Prompt-Aware Rény Kernel Entropy Diversity Guidance (SPARKE) method for prompt-awan aware diversity guidance. SPARKE utilizes conditional entropy for diversity guidance, which dynamically conditions diversity measurement on similar prompts and enables prompt-aware diversity control. While the entropy-based guidance ap- proach enhances prompt-aware diversity, its reliance on the matrix- entropy scores poses computational challenges in large-scale generation settings. To ad- dress this, we focus on the special case of Conditional latent RKE Score Guid- ance, reducing entropy computation and gradient-bases optimization complexity from the (nn²) of general entropy measures to (nz). The reduced computa- tional complexity allows for diversity-guided sampling over potentially thousands of generation rounds on different prompts. We numerically test the SPARKE method on several text-to-image diffusion models, demonstrating that the proposed method improves the prompt-awar diversity of the generated data without incur- ring significant computational costs. We release our code on the project page: https://mjjaali.giihht iotthub.i//PARKEE
Introduction
Diffusion models 1 3 have rapidly become prominent class of generative models, achieving state-of-the-art results several generative modeling tasks 2 5
Notably, their ability to produce intricate and realistic image and video data has significantly advanced various content creation pipelines [6. 7 9.. Despite these successes, ensuring sufficient diversity generated outputs remains area of active research, particularly in prompt-guided diffusion models, where the diversity of generated samples needs to be evaluated and optimized while considering the variability of the input prompts.
Diversity in prompt-guided sample generation also plays a critical role ensuring fairness and lack of mode collapse in response to certain prompt category, implying that the outputs do not collapse in response group of prompts with similar components. Therefore, an adequately diverse
"Contributed Equally
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Overview of SPARKE Method in Iteration
SD-XL (No guidance)
Previously generated
images (lteration to u-1)
Prompts:
Guidance
#19: A dog happily chasing winged
visitors town.
Guidance based
Unconditional guidance
#35: A speed-focused car with
similarity images
fiberglass shell, built for American streets.
Guidance based image similarity conditioned on prompts
#82: A lightweight fiberglass-oodied
Conditional Entropy guidance (Ours)
optimized for highways. #162: A dog leaping at birds near
European square.
SD-XL
SD-XL Unconditional Entropy Guidance
SD-XL Conditional
(No Guidance)
Entropy guidance (Ours)
iter. #19
iter. #162
iter. #19
iter. #162
iter. #19
iter. #35
iter. #82
iter. #35
iter. #82
iter. #35
iter. 482
||ll
Figure I: Overview of the proposed SPARKE method in generating images at different iterations in comparison to the vanilla Stable Diffusion-Xo -L model. We also compare the conditional-Rks guidance in SPARKE with the baseline Vendi Score guidance [10] (unconditional. in latent space).
prompt-guided generation model is supposed to provide varied and balanced outputs conditioned on each prompt category. For example, in geographically diverse image synthesis, the generation model is supposed to represent broad spectrum of regional styles, preventing overrepresentation of dominant patterns while ensuring fair coverage across different locations augmentation for visual recognition, generating semantically varied set of samples enhances the model's s generalizability and reduces biases in prompt-guided sample creation
[10]. Similarly, in data
A recently explored strategy for diversity-aware generation in diffusion models is to utilize a diversity score for guiding the sample generation. One such method is the contextualized Vendi score guidance (c-VSG) [10. The e- VSG approach builds upon the Vendi diversity measure [13]. which is a kernel matrix-bare entropy score evaluating diversity in generative models. The numerical results in [IO] demonstrate the effectiveness of regularizing the Vendi score in guiding diffusion models toward more diverse sample distributions over multiple rounds of data generation. Another method, CADS [14]
tends to improve sample diversity through the perturbation of conditional inputs, typically resulting in an increased Vendi score.
Although the mentioned diversity-score-base diffusion sampling methods apply smoothly to the unconditional sample generation without varying input prompt, a scalable prompt-aware extension to prompt- -guided diffusion models remains challenge. As discussed in [00, one feasible framework extension to comptt-guides generation can leverage pre-clustering of prompts to apply the Vendi diversity guidance separately within every prompt cluster. However, in successive queries to prompt- guided generative models, prompts often vary in subtle details, making their pre-clustering into fixed number of hard clusters challenging. In addition, relying on small clusters of highly similar prompts could lead to limited diversity across prompt clusters, due missing the partial similarities of the prompts in different clusters.

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Diversity Guidance in Latent Diffusion Models
(Existing) Guidance in the Ambient Space
(Ours) Guidance in the Latent Space
Latent Space
Latort Space
NiNece
Encoder
Decoder
Encoder
Decoder
Ambient Space
Guidence
Docodar
Doueiy Guidance
CLIP-(Ambient) Vendi Score Guidance
Latent Vendi Score Guidance (Ours)
Prompt: dog standing beside village hut Kenya Africa.
Prompt: A dog standing chasing birds along a cobblestone street Europe.
Figure 2: Comparison of latent entropy- based diversity guidance (ours) ambient entropy diversity guidance in Latent Diffusion Models (LDMs). The experiment is performed with the SD-XL LDM.
In this work, we propose Scalable Prompt-A ware Rény Kernel Entropy Diversity Guidance (SPARKE) in diffusion models, applying the conditional entropy-based diversity score family [5] of the latent representation in the latent diffusion models (LDMs). As illustrated in Figure I SPARKE directly incorporates prompts into the diversity calculation without pre-clustering. This extension enables more dynamic control over the diversity calculation with varying prompts, which can be interpreted as an adaptive bernel-based similarity evaluation without grouping the prompts into clusters. According to the conditional entropy guidance in SPARKE, we update the kernel matrix of generated data by taking the Hadamard product with the kernel matrix of input prompts. Applying an appropriate kernel function for text prompts, the updated similarity matrix will assign higher weight the pairwise interaction of samples with higher prompt similarity.
While the conditional entropy guidance offers flexibility by relaxing the requirement for explicit hard clustering of the prompts, relies on computing the gradient the matrix-basee entropy of the kernel matrix, which will be computationally expensive in large-scale generation tasks. Since the entropy score is computed for an n n kernel similarity matrix of n samples, the entropy estimation of its eigenvalues would need an eigendecomposition. leading to O(r²)) complexity. This computational cost would be heavy in settings where thousands of samples need be diversified across a large set of prompts. Thus, while conditioning diversity on prompts improves the adaptability of our proposed approach, we further need to develop a computationally scalable solution to extend the approach to a larger-scale generation of diverse data.
To improve scalability while preserving diversity-aware generation, we propose applying the order-2 Renyi matrix- based entropy, defined as the RKE Score [16]. in the SPARKE approach. This RKE- based formulation replaces eigenvalue decomposition with Frobenius norm- based entropy measure, which significantly reduces computational overhead. As result, the complexity of entropy estimation reduces to Onn²). while the gradient-baat based optimization guided diffusion models can be performed even more efficiently in ((n) time due to the canceled terms with zero gradients. By integrating these computational improvements, we introduce SPARKE framework, which maintains the advantages of prompt-conditioned diversity guidance while making large-scale sample generation feasible.
3

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Latent Diffusion Model (LDM)
LDM + SPARKE Guidance (Ours)
PixArt-E
Stable Diffusion XL
sitting quietly and reading book, 2. reading book bench, A reading book in relaxed setting. Prompts (row 2k: A.A young woman holding apple, A female holding apple and smiling, 3. A woman showing with both hands.
Prompts
Figure 3: Qualitative Comparison of samples generated by the base latent diffusion model (LDM), PixArt-E, and Stable Diffusion XL, vs. LDM guided via our proposed SPARKE guidance.
To evaluate the effectiveness of our approach, we perform several numerical experiments standard text-to-image generation models. Our results indicate that Conditional RKE Score Guidance not only scales efficiently to large number of prompts but also maintains high sample diversity while preserving fidelity. Compared to prior methods, our approach achieves a more balanced trade-off between diversity and computational efficiency, making suitable for real-world generative modeling applications that require scalability. The following is a summary of the contributions our work:
We introduce the conditional entropy score guidance prompt-aware diversity promotion tool in sampling from diffusion models.
We propose using the order-2 Renyi kernel entropy (RKF) score to reduce the computational complexity of the entropy-based diversity guidance.
We propose the application of entropy guidance the latent space of latent diffusion models, improving the efficiency and performance in the entropy-based diversity guidance (See Figure 2
We test our method on several state-of-the-ar diffusion models (see Figures 3) and text-to-image benchmarks, indicating its ability to improve sample diversity and computational efficiency.
2 Related Works
Standard and Latent Diffussin Models. Diffusion generative models 2 [7] 3 learns to reverse an iterative noising process, effectively estimating the gradient of the data log-density (the Stein score (18) to generate new data samples. This approach has shown remarkable capabilities in synthesizing high-fidelity images [6
19 20 Despite the impressive results, primary limitation of diffusion models was the substantial computational cost, particularly when operating directly in ditennsinaii spaces like pixel space. To address this challenge, Latent Diffusion Models (LDMs)) [4] 21) perform the forward and denoising processes in an encoded latent space, enabling high-quality images such as Stable Diffusion [4 [5] and video (22 23 g synthesis at large scale.
Conditional Generation with Guidance. The ability to control generative processes with specific conditions is increasingly crucial for practical applications, based on conditional inputs like text-

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class labels [6]. style images 226 27 or human motions 22), etc. Methods for conditional generation with guidance are categorized either training- based or training-free free. Training- baaiid approaches either learn time-dependent classifier that guides the noisy sample
guided [20 24 25
25 or directly train the conditional denoising model c0(2r, 1, y) via few-shot adaptation 226 4 30 In contrast, training-free guidance aims at zero-shot conditional
towards the condition y 66 24 29
generation by leveraging a pre-treeeee trained differentiable target predictor without requiring any training. This predictor can be a classifier, loss function, or energy function quantifying the alignment of 3. Our work can be included as a training- guidance approach that applies conditional entropy scores guidance to enhance the diversity of samples.
sample with the target condition 31 [3d
Quantifying Diversity and Novelty. Diversity is quantified using both reference-basee
[35] [6] and the RKE score
reference- free metrics. Reference-free metrics include the Vendi Score [3 37| 38],
16 for unconditional models, and the Conditional-RKE: 15] and Scendi 39 scores for conditional models. Also, the diversity metrics have been extended to online and distributed model selection tasks
analyzes how generated samples differ from a reference model, with 45 46 proposing a spectral method to measure the entropy of novel modes. 50] also introduce kernel-based methods to compare and align two embeddings. In this work, we propose a novelty guidance approach that operates with respect to reference dataset.
40
45 For novelty, prior work 44
45 46
47 48
49
Guidance for Improving Diversity. A common strategy in diffusion- based generative modeling is the use of guidance mechanisms to balance quality and diversity [51] 52 [3] For example, classifier-free guidance methods [52] considerably enhance prompt alignment and image quality but often compromise diversity due to overly deterministic conditioning. Several works have attempted to address this diversity challenge. To encourage diversity, 54 introduced strategy that samples from the data manifold's low-density regions, however, their method operates directly in pixel space, posing challenges in adapting it effectively to latent diffusion frameworks. Another line of work is fine-tuning, In [55], the authors provide a finetuning method using Reinforcement Learning to improve the diversity of generated samples using a diversity reward function.
Recent works tackle this problem in the denoising phase. The CADS framework 14| shows that adding Gaussian noise the conditioning signals during inference increases sample diversity. Particle Guidance (PG) [56] employs non-lID sampling from the joint distribution defined by a diffusion model combined with a potential function that maximizes pairwise dissimilarity across all samples, independent of semantic context. Similar to PG, ProCreate (7) uses DreamSim embeddings to find similar images via log energy and maximizes embedding- -sppddeeinn-peeeeeeeeeeeee distances. The concurrent method SPELL (58) adds repellency terms during sampling to prevent samples in a batch from being too close. These methods maximize across all samples without considering the prompts. However, these methods are prompt-agnostic, while ours dynamically conditions diversity guidance on the input.
The recent work [10] introduces contextualized Vendi Score Guidance (c-V,G), enhancing generative diversity during the denoising process using Vendi Score [13). Their approach, however, requires the same prompts, restricting its applicability across diverse prompt scenarios. To tackle this issue, (TS] uses Conditional-Vendl score guidance for prompt-aware diversity guidance. On the other hand, our method leverages the RKE Score [16] to significantly enhance computational efficiency and sample complexity. Additionally, we propose prompt- guidance inspired by [15), enabling adaptive soft-clustering and effective conditioning on semantically distinct prompts. Moreover, unlike [0), which applies guidance based on latent encoded features of reference images, our strategy directly applies guidance within the diffusion model's ''s latent space, saving computational costs and enabling a prompt-aware diversity improvement.
3 Preliminaries
3.1 Kernel function and Vendi diversity scores
Consider a sample x E X' in the support set X. A function k: ; X' x - IR is called kernel function, if for every integer N and sample set {21, 3 E X, the following kernel similarity matrix K E [R is positive semi-definite (PSD):
k(11,
x(x1,In))
Kx =
(1)
k(#n,
2()))
5

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We assume that the kernel function is normalized, i.e., k(æ,z) 1 for every X. For general (potentially unnormalized) kernel k can define its normalized counterpart k(x,y) k(z,y) / k(x, 2) k(y, y), which we apply whenever normalization is required. The Rényi Kernel Entropy (RKE) diversity score [16) is defined and analyzed as the inverse Frobenius norm-squared of the trace-normalized kernel matrix:
RKEETL Rn) == exp( ex (*)()))())) |
(2)
where ||
|| denotes the Frobenius norm. As theoretically shown in [16], the RKE score can be regarded as mode count of mixture distribution with multiple modes.
To extend this entropy- -ased diversity scores conditional (i.e., prompt-aware) diversity mea- surement for prompt-guides generative models. [[3] propose the application of conditional kernel matrix entropy measures, resulting in the following definition of order-2 Conditional- given the Hadamard product Kx @ Kr of the output data Kx and input prompt Kr kernel matrices:
||
Conditional-RKE| T1..... Fni t1 ,I....,tt fn)
(3)
Kx O Kr 2
Note that here the Hadamard product of the prompt (t1.... tn) kernel matrix Kr and output (x1,... kernel matrix Kx is defined as the elementwise product of the matrices, which is guaranteed to be PSD matrix by the Schur product theorem.
3.2 Conditional Latent Diffusion Models
Latent Diffusion Models (LDMs) 4 can achieve scalability and efficiency by performing the diffusion process within a compressed latent space, rather than directly in pixel space. A pre-trained autoencoder used in LDMs, consisting of an encoder & and decoder D. The encoder maps high-dimensional images E R "* x to a lower-dimensional latent representation 2a E(x) E Rhxwxe while the decoder reconstructs the images á D(zn) from a denoised latent variable Zo- The forward diffusion process applies in the latent space as 2, 20, + vT 0r where 6, ~ (O, f) and Og E are predefined noise schedule parameters. Then the conditional L.MMs with conditions y are trained to predict the noise E0 t, y) at each time step t, also learn the score of Pe(ze y) [7 3]:
min E. F. [100(2),)))) <x = min Ez, Ei,yy [1100(2,),))) vI az V= (o
4 Scalable Prompt-Awar Diversity Guidance in Diffusion Models
Utilizing the kernel-based entropy diversity scores and latent diffusion models (LDMs) described in Section (.22] we introduce a scalable conditional entropy-based framework extending the recent Vendi score-based approach (10] diversity-guider generative modeling to prompt-aware diversity enhancement that suits the conditional text-to-image models. Specifically, we first propose extending the order-1 1 Vendi score to the general matrix-based order-a Rényi entropy and subsequently to the conditional order-a Rényi entropy for achieving higher prompt-conditioned diversity. In addition, we demonstrate a computationally efficient special case in this family of diversity score functions by considering the order-2 entropy measures. This choice of entropy function leads to the RKE-guidance and Conditional-RK: guidance approaches for enhancing overall diversity and prompt-aware diversity in sample generation via diffusion models.
4.1 Diversity guidance via general order-a Renyi Entropy and RKE scores
The existing diversity score- based guidance approach, including the Vendi guidance in 10, optimizes the diversity score of the embedded version of the generated outputs, e.g. the CLIP embedding (59) of image data generated by the prompt-guided diffusion models. However, such a guidance process top of the diffusion model is computationally expensive and may
by considering an embedding not lead semantically diverse samples. As discussed in [3 37 computing the order-1 Vendi score and its gradients requires at least 2.307 computations for samples, and in practice involves

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O(n") computations for the sigen-decompositions of kernel matrices. This computational complexity limits practical window sizes of the existing Vendi guidance approach to few hundred samples, i.. the guidance function cannot be computed by standard GPU processor for sample size >> 500.
To reduce computational complexity, we extend the order-1 Vendi score guidance the general order-a Renyi kernel entropy, and adopt the specific case = 2, referred to as the RKE score [16]. This formulation significantly lowers computational cost and defined as:
(RKE(=!)) 1............................. ,...,, 2..),, 1/4 K*
|
E (2 20)) -=))))
(5)
with kernel matrix (K2).; 1(2(1,,) 20) computed directly for the latent representations and
denotes the total number of generated samples. Therefore, applying CRKE as the guidance potential function reduces the computational complexity from (n²) in order-1 Vendi score to O(n²), enabling significantly larger batch sizes during the guided sampling process and resulting in higher efficiency.
4.2 Diversity-Guidee Sampling in Latent Diffusion Models
In contrast previous work using order-1 Vendi score as the diversity guidance in ambient image space [10]. we integrate efficient IRKE score diversity guidance directly into latent-space sampling. Standard LDMs employ classifier-free guidance (CFG) (52) for conditional sampling, iteratively denoising latents z from the noisy latents 2; at time step & via reverse samplers:
Zt-1 Sampler(ze z,, éØ (z y)),
(6)
To efficiently promote diversity within the latent space, we optimize the Inverse-RKE (IRKE) score loss. Proposition [ defines this loss and its gradient:
{ denote set of generated data. Let kernel function k: Z 2 - TR be symmetric and normalized, i.e. k(z, for every 2. Then, we observe that the function CRKE(=(1), (()) in Eg. (5) changes montonically with the Inverse-KKE RKE.stttiionnnn
Proposition 1. Let Z = (2(1), (2)
LiRKE(2(1) (n)) L/RKKE ,...,, (n), whose gradient with respect to (n) is:
I k(
V vi(n) CIRKE
2 k(2 x(1)).
The above Proposition iimplies that an optimization objective maximizing LRKE to promote diversity can be equivalently pursued by minimizing LIRKE, reducing the computational complexity from O(n²) to (n). Leveraging this computational efficacy, our approach directly updates the gradient of LIRKE rather than computing the gradient of <RKE to the latent (*)), allowing for an efficient, explicit diversity-promoting update. Specificallyy, for Latent Diffusion Models (LDMs), we introduce the following diversity-guides sampling via Eq. in each time step t:
Zt +- 2t 11
(n) LIRKE
(IRKE Diversity Guidance)
(8)
where 7) represents the guidance scale and n denotes the number of previously generated samples.
4.3 Conditional Prompt-Aware Diversity Guidance
To explicitly capture prompt-conditioned diversity and focus on the computational efficiency of order-2, we introduce the Conditional RKE loss:
|r 2
LCond-RKE
(n), y (1)
(m))
| o Kzll
where (Ky), = ky (y) (((0).) (() denotes the similarity among condition (e.g., prompts) embeddings. Similarly, reduce the computational complexity from O(n²) to ((n), by computing the gradient of Conditional Inverse-RKE (Cond-IRKE) defined in Proposition 2
Proposition 2. Let Z. denote set of generated data, and Y (1( corresponding conditions. Let the kernel function i be symmetric and normalized. Then, we observe that the function LCond-RKE (1) ....., (1) (1)) ...., ....y(())) in Eq. (9) changes montonically with
(n)) is the set of
7

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Algorithm 1: Scalable Prompt-Aware Latent IRKE Diversity Guidance
Input: Latents (z(")...., 2 2n prompt features (y(*)... ..... " }. kernel functions kg.
ky, denoising model co. diffusion reverse sampler, guidance scale w, diversity guidance scale 77, decoder D
Output: Diverse generated samples (i) with prompt features (n)))
for f to 1 do
Compute CFG guided noise: Eg = (1 + w) co(z)") (m) (n)
tt f.y(")) - w . co(2, ,t)
Perform one-step denoising: 2;-1 t Sampler(z, (m) (()))
3
Compute z. Ky, and Loond-IRKE | O Ky
F
Compute the gradients g(m) = Vz(n Loond
Update latents: z +- 2 17 17. g(m);
(n)
7 Decode final samples: (n)) D(2))))
DDIM Deasity: 103 = 0.020
CADS Density: 0.57 = 0,813
V-V Density: 0.99 = 0.010
Particle Guide
SPARKE (Ours) Deasity: 8.99 = 0.006
Density: 0.% : 0.013
Coverage:
Coverage:
Coverage:
Coverage:
Coverage:
Density: 0.93 0,017
Density: (182 0.013
Density: 0U86 0.009
Density: 0.94 0.012
Density: 0:94 0.207
Coverage: 0.20 0.014
Cuverage: 0.46 0.017
Coverage: 0.33 0.011
Coverage 0.74 0.015
Coverage: 0.50
Figure 4: Comparison of SPARKE (Conditional RKE) Guidance with baselines on 2D GMMs.
the Conditional InverseRKEE function CCond-IRKE (1) 2 (m) (m):)(1) yod) = [Kz o ly whose gradient with respect to 2(n) is:
(n) Coond-IRKE OX
kz (0)))) (g) (n)) zin kiz (z(2))) 20)) (n)).
(10)
Then we propose the following prompt-aware guidded sampling via Eq. 10 in time step t:
Z: - Z: 7) Vztn) Coond-IRKE
(Cond-IRKE Diversity Guidance)
(11)
Algorithm T provides an explicit outline of this procedure. This Cond-IRKE guidance explicitly aligns the diversity of generated samples with respective prompts, while significantly maintaining the computational efficiency in gradient calculation. In Appendix B.3 interpretation based on stochastic differential equation.
we provide a theoretical
5 Numerical Results
We evaluated the performance of the SPARKE framework on various conditional diffusion models, where our results support that SPARKE can boost output diversity without compromising fidelity scores considerably. For the complete set of our numerical results, refer to the Appendix [
Baselines. We compare our method with CADS 14, Particle Guidance [56), and Contextualized Vendi Score Guidance (c-VSG) [10]. In experiments without reference, use VSG [10].
8

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Table 1: Quantitative comparison of guidance methods Stable Diffusion 2.1.
Method
CLIPScore KDx10²
Cond-Vendi Vendi Score 1 Vendi Score
In-batch Sim.x
SD (No Guidance) 60
31.20
52.37
26.54
369.37
80.36
e-VSG
28.75
56.25
27.91
376.48
79.82
CADS
14
29.89
55.08
28.73
380.08
79.44
latent RKE Guidance (Ours)
30.18
55.37
29.88
387.59
79.01
SPARKE: latent Cond-RKE (Ours)
30,96
53.15
32.57
405.51
75.68
Stable Diffusion 2.1
Prompt-Unaware Diversity Guidance
SPARKE: Prompt-Aware Diversity Guidance
(RKE score)
(Conditional RKE score)
In-batch Sim.: 79.01
In-batch Sim. 75.68
Prompts: iter #6219; This is image of bench overlooking beach, (2) iter N6337: white bench sitting that overlooks view, (3) iter #9353.A white wooden bench sitting on green hill next to the ocean.
D
Prompts: (1) iter 47927: a blue plate with an orange a cracker some lettuce and twist bar, (2) iter #8354: A dish contains an orange and snacks, (3) iter #9287: An orange, chocolate, cracker, and piece of lettuce on a plate
Figure 5: Comparison of SPARKE prompt-aware diversity guidance via conditional- RKE score vs.
diversity-unaware diversity guidance using the RKE score SD 2.1 text-to-image generation.
Models. We used Stable Diffusion [60] and the larger-scale Stable Diffusion XL (SDXL) (5) and PixArt-> 6l in our experiments on text-to-image generation. We also provide additional experimental results on different SOTAs in the Appendix.
Evaluation. We compared our method with baselines in terms of output diversity and fidelity. Fidelity was measured using CLIPScore [62], and KID [63] to evaluate prompt quality and consistency, and Density [36] where reference dataset was available. For diversity, we used Vendi [13] and Conditional-Vett Vendi [15] scores, and we used Coverage (36) when a reference dataset existed. We
measured diversity within each prompt cluster using the in-batch similarity score [56), calculated as the average pairwise cosine similarity of image features in a batch.
Synthetic Datasets. We compare method on 2D Gaussian mixture benchmarks [64], training a diffusion model with the DDIM sampler (65 and fine-tuning hyperparameters (see Appendix C). Figure 4 shows that CADS covered the modes' support but with slight distribution shift, while c- VSG better adhered to the modes at the cost of lower diversity. PG and SPARKE both covered the modes well, with SPARKE producing fewer noisy samples due to its clustering busseriig-based structure.
Comparison of Entropy Guidance Effeett in Latent and Ambient Spaces. We compared latent- space guidance (SPARKH) with CL.P-embedded ambient-space guidance from VSG [10] using modified GeoDE categories (66] As qualitatively shown Figure 2 CLIP-ambient led to visual artifacts and offered less improvement in output visual diversity, while latent guidance produced more semantically diverse outputs. We also provided quantitative results in Table 5] which show that latent guidance achieves higher diversity. Also, latent guidance requires significantly less GPU memory (=20GB vs. =35GB) offering substantially better computational efficiency.
Comparison of Prompt-Aware Diversity Guidance vs. Unconditional Guidance. We generated images for 10,000 MS-COCO prompts (67] using Stable Diffusion 2.1, comparing latent RKE condi- tional guidance prompt--waree against unconditional RKE guidance (prompt-unaware). Figure shows unconditional diversity guidance becomes less effective over time, while SPARKE's prompt- aware approach remained effective throughout all 40k iterations. cobferms that prompt-aware

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Table 2: Comparison of diversity and fidelity metrics across different models and methods
Method
CLIPScore
KDx10
Cond-Vendi Score ?
Yendi Score
In-batch Sim. x10%
SDXL
31.17
66.37
27.54
309.54
81.67
SDXL SPARKE
30.47
62.62
31.17
313.80
77.75
PixAr-EE
31,01
65.37
26.45
307.36
83.84
PixAr--) SPARKE
30,66
63.86
32.14
322.25
78.81
Novelty Guidance Using SPARKE
Reference Dataset
Latent Diffusion Model (No Guidance)
Others 37%
(Cats and Dogs)
Cats/Dogs 63%
Latent Diffusion Model + SPARKE Guidance (Ours)
Cats/Dugs
Others 85%
Figure 6: Novelty guidance with SPARKE. Using the prompt "A young lady walking with an animal in the park," samples are generated with respect to a reference set of cat and dog images, resulting in more novel samples compared the base model.
methods achieve higher diversity while preserving image quality and prompt alignment. Also, Table 2 provides the quantitative results for SD-XL and PixArt-
Novelty Guidance Using SPARKE. guide an SD-XL model with reference dataset approach successfully reduced the generation of cats and dogs, yielding more novel samples with respect to the reference dataset and resulting more balanced distribution of other animals.
We evaluated novelty guidance by using the SPARKE method
and dog images. As shown Figure 6 this
Computational Efficiency Comparison. We evaluated SPARKE's computational efficiency by comparing its runtime and peak memory with the baselines over 1000 text-to-image generations using a 50-step diffusion process on an NVIDIA RTX 4090. The results, as shown in Table 3 indicate that SPARKE requires significantly lower runtime and less memory it functions in the latent space).
Table 3: Comparison of runtime and GPU memory usage for different guidance methods.
Model + Guidance Method
Runtime per sample (s)
GPU Memory Peak (GB)
Stable Diffusion v1.5
1.620 0.265
3.178 i 0.001
SD-1.5 SPARKE (Ours)
1.752 + 0.287
3.230 + 0.025
SD-1.5 c-VSG
3.079 0.296
8.665 1 0.116
SD-1.5 Particle Guide (Pixel)
4.912 + 0.312
7.531 + 0.032
SD-1.5 Particle Guide (DINOv2)
9.102 0.271
20.133 + 0.038
Conclusion and Limitations
In this work, we proposed the prompt-aware SPARKE diversity guidance approach for prompt-based diffusion models. The SPARKE method aims to improve the diversity of output data conditioned on the prompt, so that the diversity guidance process takes into account the similarity of the prompts. We also proposed the application of RKE and Conditional- -KEE scores in the latent space of LDMs boost the scalability in the SPARKE method. Our numerical results of applying SPARKE the stable- diffe-diffusion LDMs indicate the method's qualitative and quantitative improvement of variety in generated samples. limitation of our numerical evaluation its primary focus on image generation diffusion models. Future exploration can extend SPARKE's application other modalities, such as video and diffusion models. Furthermore, combining SPARKE's entropy guidance with other techniques for diffusion models presents another interesting future direction.
10

---

Acknowledgments
The work of Farzan Farnia is partially supported by grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by CUHK Direct Research Grants with CUHK Project No. 4055 and 4937054. The work of Amin Gohari is supported by CUHK Direct Research Grants with CUHK Project No. 4055270. The work also supported by grant under 1+1+1 CUHK-C CUUIIKCCHHKZZ--OCCC -DSTC Joint Collaboration Fund. Finally, the authors would like to sincerely thank the anonymous reviewers for their insightful feedback and constructive suggestions.
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15

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A Preliminaries on Diffusion Models
A.1 Denoising Diffusion Probabilistic Models (DDPMs)
Denoising diffusion probabilistic models (DDPMs) 2 define a generative process by reversing fixed Markovian forward diffusion that progressively adds Gaussian noise data. Given data sample Zo (2())), time step t [T] _ {1, (I...., T), the forward process gradually adds noise to construct a noisy data point Dt = Vo + ví - d,ét, where e, ((,, I) is standard Gaussian noise and Or, [0, 1] monotonically decreases with time step l control the noise level. The diffusion model 6g X' x [T] + X' is trained to predict the noise E, at each time step I, also learn the score of
Pe (2
min E En, [IE0((0,,1)) Ex = min eor
|| 1) + v ar Va, log logp1(=>))12 (12) (+,)
The reverse process obtained by - ~ Pt- llll [4 multiple efficient reverse samplers are proposed 65 sampler, we sample F by:
is not directly computable in practice, In the commonly-used DDIM 65
68
69
21
Va,Tor V1
-t-1 10 + V 1 0--1
of
+ t.ct,
(13)
where of is the DDIM parameter, and the clean sample Zoju given H, is estimated according to Tweedie's 's Formula 77 71):
vI anes(1
Toje
(14)
Var
A.2 Conditional Generation via Guidance.
In conditional generation tasks like text-to-image synthesis, diffusion models learn to approximate the conditional distribution p( (y) given conditions y (c.g., text prompts). From the view of score functions [17 3 we denote the conditional score as:
s2, log ( Vzz log V az loo Pr (Brlaz))
(15)
Conditional
Uncunditional Score
Guidance
The strategies of conditional generation via guidance can be roughly divided into two categories: Training-basce methods and training-free free methods.
Training-based Guidance. Training-basse based guidance methods include several strategies. One approach, Classifier- Guidacce,, initially proposed in [3 (). requires training an additional time- dependent classifier to estimate the guidance score f(æ,, t) - Em f#o) x= f(zo). Alter- natively, other training- based techniques involve few-shot fine-tuning of base models or the use of adapters 4 30 achieve conditional control.
distinct yet training-basse based approach is Classifier- Freef Guidance (CFG), introduced by 52 Unlike methods requiring separate classifier, CFG integrates the condition y as direct input to the conditional denoising network e
c (Ie, t. y). It is enabled by a joint training procedure where the model also learns to make unconditional predictions by randomly dropping the condition with specific probability during each training iteration. During inference, CFG estimates the conditional noise prediction follows:
éø( t, 3) (1+ w) cg( y) c0(
(16)
where the guidance scale w adjusts the strength of conditional guidance. These various training- based guidance methods have demonstrated considerable effectiveness with the availability of training resources.
Training- Guidance. An alternative category for conditional guidance is training-free guid- ance. Instead of requiring additional training, these methods directly introduce a time-independent conditional predictor ff on the estimated clean data f ( y). which can be classifier, loss func- tion, or energy function quantifying the alignment of generated sample with the target condi- Then the estimation of the guidance score via training-free free approaches is:
tion 32 33
72).
V æ, log (
-aa,f (ūo)).)).
(17)
16

---

where the clean sample for the predictor is estimated by Tweedie's ' Formula 70 71
3t v1 0460 (2;, 1)
Toit
(18)
V
B Proofs
B.1 Proof of Proposition
Proof. Let Kg be the kernel matrix with entries (Kz)) = The RKE loss is given by:
2²
CRKE 2 (1)
(19)
1|x111
Li=1 ΣØ=1
The Inverse-RKE, function LIRKE is defined by:
k(z(1) z 2
Lj=1
CIRKE (n))
(20)
CRKE (....,)))
Tr(Kz)²
Given that the kernel function k is normalized, i.e., x), = for z E Z, the trace of the kernel matrix Kz is:
Tr(K2) Σ k(z(1) (11)
n,
1=1
Substituting this into the expression for CIRKE(Z(1
;...; (m) in Eq. 20
(iRKE(
2 (1)))
1
k(2
(21)
n
1=1 j=1
Now, we want to compute the gradient of LIRKE(2
z (n) with respect to z (m);
(n) LIRKE (()), = V
k k(z10) 00)2
(22)
n²
im
Since 1/n² is constant with respect to (n));
V 2() LIRKF (2)) (n))
1 Vz())
V
Σ>
k(z(0, 26102
(23)
n²
Let S = E==E" 2())) We need to find V 2iin) S. The terms in the sum S that involve (xx) are those where = n or j = n (or both). We can split the sum into:
n-1 1=11-
S Σ
k(2(0) 200 (Terms not involving x 2(n))
+ (()))
(j= -=mni + n)
+ Σ ((>(n),2 2002 (i= n, + n)
+ k(2 (m) (i=n,) = =
Using the symmetry of the kernel, k(> (n), x()) k(2(1), (m))), the second and third sums are identical:
n-1
S
k(= 2 00 + 2
Σ
((=(1t)=(1)))) k ((((ا) (())²² + +((((m) (())))
(24)
1=1
17

---

Now, we compute the gradient of S with respect to 2(");
R-in-1
2-1
V 2x; S= ((())
ΣΣ k(=(0, 2(2(), + +V (
2 3 (2200,
+Vz(0) (k(2(m), 2(0))))
(25)
The first term is zero because it does not depend on (()), For the second term:
a-1
Σ
k(z(1) (6) 2 (n))3
2 2(1) (k(2!"), ( 2(11)2
g(n)
2
2k(221) (0) z 211) V 2(0) k((2 2()))
(26)
= 4 Σ k(z(1), (1)) 2t k(z (1)).
For the third term, since k(z, = 1 (normalized kernel,, this term is constant:
V (n))
[1(2((1) (m) z (n))²) = V V200 (13) = V sin) (1) = 0,
(27)
According to Eq. (26 and Eq. 27 we have the gradeitn for S:
(n) S k02((), 2(1)) 22m) 21)))
(28)
Substituting this back into the gradient LIRKE (z (1)
,..,, (n)) in Eq. 23
V (m) (IRKE(Z (2.,,,,),,,))))))))))))) (n))
(1))
k(2 (1) z (n) V 2(( x(m))
112
(29)
Σ k(z(0, (m) v k(2 ((()),
n
Since 4/n² is positive constant (for n 2 1), we have the following:
n-1
( LIRKE x
Σ k(z (n)
( Venn) (0)
(30)
This proves the form of the gradient.
Regarding the monotonic relationship LIRKE = L/LKKE CRKE is always positive (Tr(Kz)² n 0 and the denominator Σ kij O; for it be non-zero, not all kernel values can be zero), then CiKE > 0. Therefore, dCasn
< O, which means that LIRKE is strictly monotonically decreasing function of LRKE. This completes the proof of Proposition 1.
dC
B.2 Proof of Proposition 2
Proof. Let Kz be the kernel matrix for the data with entries (Kz)iş = (z)()(0) 20)). Let Ky be the kernel matrix for the conditions with entries (Ky)s )ig = ky (z ())). The normalized kernel matrices are K K Kz/Tr(K2 and Ky Kr/Tr(Ky). Given that the kernel functions kz and ky are normalized, their traces are:
Tr(Kz) = Σ (2)
(1)
1=
i=1
t=1
Tr(Ky)
Σ
by
(8)
1=n n
1=1
18

---

So = and Ky Ky/n. The Conditional Inverse-RKE function is defined as:
(m) (0)) ,...., (())
[R @ Ky l
(31)
where @ denotes the Hadamard (element-wise) product. The entries of Kz @ Ky are:
(Kz o Ky); (K2)in (Ky);
kz(2 (0, ,00)) - (x
1
(32)
,z(200² =()) (0))
n
The squared Frobenius norm is the sum the squares its elements, then we have the following according to Eq. 31
kz (z (0) 22 kx (3) y00))
LCom IRKE (2:Y)= =
712
i=1 j=1
(33)
kz (z (1) z()) Noy (2) y0
1=
Now, we want to compute the gradient of CCond-IRKE (2; Y') with respect to (nn) according to Eq. (33)
V (n) LCond-IRKE (2:Y)
n
1
z(n)
ΣΣ f=
20)) ( 0
(34)
Let Sc = E. Eラ= liz kz((00) 200)) (0) (0) 2 We need find V 22( Sc. The terms in the
sum Sc that involve (") (through kz) are those where = n or j = n (or both), and the terms ky (x((), yl)) do not depend on 2 2(1). We can split the sum as follows:
n-1n-1
Sc = ΣΣ
kzz (z x0))) (0)
(1) y 02
(terms not involving ((n)
kz (1) x
(2)
(j = n, + n)
(35)
+
Σ (z() , 220))kkr (m)) 20)
(i = n, # n)
1-1
+ (x) yky (n) (n)), (i = n,j n)
Using the symmetry of the kernels, 22 (m) 2(1) by (g()) y(n) (n)), the second and third sums are identical. Then we have:
, and (1)))
Sc
kz(=(1) 2(0)) (60))kk((0 (y) (g))
(36)
+2 2 Σ kz (1), 2 (()))kky (x))) y m0) + kz()(m) 20) ) (m) (n)))
Now, we compute the gradient of Sc with respect to (n))
n-
So =V 2(n)
kz (0) 200 (1)))))))))))), gong
(37)
V 2(m)
2 Σ
(z( ((1) (o)))
V (n)
V(n)
(x)() z (m)) 2ky (7))))
19

---

The first term is zero because it does not depend on z 21)), For the second term:
V Vz(n)
2 k (z(1) 2211)) ( (
2
by (y yy v 20n)) (kz(2(0)2(1))
by (y (0) (2))) (2 22 2(1)) Vzin 21)))
2
n
Σ
kz (z (1), xz 21))) ky yy (/n k2 (2(() ,(())
(38)
For the third term, since kz2(2(n) 2(1)) = 1 and ky (g) (m))) (normalized kernels), this term constant:
(()) (Kz(z(m), (2)))) Ky (1) 1 (())))) V Va(n) (12 12) 2 0,
(39)
So have:
71
(n) Se =
kz(z(1) (1), ((m)))y (2 (1) 2
(40)
Substituting this back into the gradient of L IRKE (2:Y) Y) in Eq. 33
V (n) Coond-IRKE (2:Y)=
1
4
kz (z ky)) (1 (1) y (m)) 2t kz(x0) x
x0(0)
n
(41)
4
Σ
kiz (z (,) (kr)kr(( (z) (n))) 2(11),
n
Since 4/n² is positive constant (for n 2 1), we finally get:
n2
20( LCond-IRKE OX
kz(2 (m) by (n) (2)
(42)
This proves the form of the gradient. Regarding the monotonic relationship: From Eq. 99. we have:
Ky
LCond RKE (2:Y)
(43)
||
Ky Ti(K Rz)
We have shown that Tr(Ky @ Kz) n. since (Ky Kz)N ky (y (x (0) 1. 1. Also, Ky
12 = |K / = |Kr
Substituting these into the formulation for
LCond-RKE in Eq. 433
マe Ky
+
Ky
|k
(44)
K2
Ky
O Kzl1
|Ky 3 Kz
F
From the definition of LCood-IRKE YY;Y) in Eq.
31
we have:
Kz
KY 2
1 nd [k o kr
LCond-IRKE (2; Y) [k z ④ Kyl
(45)
n
Let Cy = || This term depends only on the conditions Y and is constant with respect to 2(n), Cy- is always positive since the kernel function Ky is positive semi-definite and not all kernel values can be O. From the formulation for LCond-IRKE in Eq. (3I). we have K| O Ky = n (Cond-RKE(ZZY) Substituting this into the formulation for LKond-RKE:
Cy
Lcond.RKE ( (2:Y)=
(46)
12 LL IRKE Y2
Since Cy /n²" is positive constant, then LComd RKF Z; Y) is strictly monotonically decreasing function of CCond.IRKE (2; Y). Thus, they change monotonically with respect to each other. This completes the proof of Proposition 2.
D
20

---

B.3 Interpretation of SPARKE
Our method, SPARKE, can be theoretically interpreted as an interacting particle system where sequential samples z (2), 2 1.., 2(n) evolve along gradient flow to minimize energy potential,
thus improving prompt-aware diversity. This process is described by the following sequential stochastic differential equation:
dz (m) = - f(2 ,1) ((1)) (V2in) log lo - 17 Vain) ICood IRKE (Z1, (Z1,.... 2n) 2
dt dt+g(t dd,,,
(47)
The core insight of SPARKE is to employ the Conditional Rényi Kernl Entropy (Conditional RKE) as a differentiable objective for promoting diversity. Following [T6], the order-2 RKE score serves a differentiable objective for counting the modes of particle distribution. Furthermore, the Conditional RKE score in [15] quantifies the internal diversity conditioning on the prompt categories. SPARKE defines a gradient flow that optimizes the Conditional RKE score, and sequentially drives samples to cover distinct modes, while the conditional mechanism ensures the prompt-aware diversity guidance potential.
C Implementation Details and Hyperparameters
In the kernel-based guidance experiments of SPARKE and the baselines with kernel entropy diversity scores, we considered Gaussian kernel, which consistently led to higher output scores in comparison the other standard cosine similarity kernel (see Section D for ablation studies). We used the same Gaussian kernel bandwidth a in the RKE and Vendi experiments, and the bandwidth parameter choice matches the selected value in [5 13. The numerical experiments were conducted on 4VNIDI GeForce RTX 4090 GPUs, each of which has 22.5 GB of memory.
C.1 Experimental Configuration for Table
We evaluated the methods listed in Table the following setting. We used Stable Diffusion 2.1 with a resolution of 1024x 1024, a fixed classifier-fre guidance scale of WcrG = 7.5, and 50 inference steps using the DPM solver. We used the first 10,000 prompts of the MS-COCO 2014 validation set and fixed the generation seed to be able to compare the effect of the methods. For the methods, we used the following configuration to generate the results reported in Table
The hyperparameter tuning was performed by performing cross- pross-validation on the in-batch similarity score, selecting the hyperparameter values that optimized this alignment-based metric. Note that the in-batch similarity score accounts for both text-image consistency and inter-sample diversity as discussed in (56). Due to GPU memory requirements (as mentioned in Section B.2 in (56)), we were unable to evaluate the Particle Guide baseline [56] on SD 1 Following the provided implementation of this baseline for SD v1.5, we conducted this baseline's 's experiments only on SD v1.5.
Stable Diffusion. We used the standard CFG guidance and DPM solver with no additional diversity- related guidance.
CADS. Following the discussion in Table 13 of [1,, we set the threshold parameters as 71 = 0.6 and T2
0.9, 16 = 1, and used a noise scale of 0.25.
V-V. We note that the reference 100 considered GeoDE (66) and DollarStreet 73 datasets, in
which multiple samples exist per input prompt. On the other hand, in our experiments, we considered the standard MSCOCO prompt set where for each prompt corresponds we access a single image, making the contextualized Vendi guidance baseline in [10] not directly applicable. Therefore, simulated the non-comtextualized version of VSG. For selecting the Vendui score guidance scale, performed validation over the set (0, 0.04, 0.05, 0.06, 0.07). following the procedure in [TO]. A guidance frequency of 5 was used, consistent with the original implementation. To maintain stable gradient computation for the Vendi score, implemented a sliding window of 150 most recently generated samples, as gradient calculations became numerically unstable for some steps beyond this threshold.
latent RKE Guidance. We used a Gaussian kernel with bandwidth asmg 0.8 and used r = 0.03 as the weight of RKE guidance. To balance the effects of the diversity guidance in sample generation,
21

---

Input
Input#1
Input #2
x
x
x
Input #1
X
Input #10
x
x
X
X
X
X
Input #6
x
X
Input
x
x
x
X
11
Figure 7: Illustration of input-based Gaussian output used for the conditional diffusion model in Figure As displayed, the output 2D Gaussian vector is generated centered around the mean vector specified by the input prompt number.
the RKE guidance update was applied every 10 reverse-diffusion steps in the diffusion process, which is similar to the implementation of Vendi score guidance in [TO]. Unlike VSG, which requires a sample window limit, RKE guidance operates without window size constraints, leveraging the complete history of generated samples for gradient computation.
SPARKE (latent Conditional RKE Guidance). We considered the same Gaussian kernel for the image generation with bandwidth Ging 0.8 and used bandwidth parameter Øext = 0.3 for the text kernel. The guidance hyperparameter was set to 7) 0.03, as in RKE guidance. Similar to the RKE and Vendi guidance, the SPARKE diversity guidance steps. Unlike VSG but similar to RKE, SPARKE uses the complete history of generated samples for guidance.
applied every 10 reverse-diffusion
C.2 Experiment Settings the results of Table 4an Figure
We conducted additional experiments using Stable Diffusion v1.5 with a resolution of 512x512. We created prompt set by performing K-Means clustering on the MSCOCO 2014 validation prompts. Specifically, we clustered the MS-COCO prompt dataset via the spectral clustering in the CLIIP embedding space, into 40 groups and randomly drawn prompts from each cluster, resulting in total of 2,000 prompts. To evaluate the performance of our method with the baselines with different seeds, we generated five samples per prompt using seeds 0, 1, 2, 3, and 4, yielding a total 10,000 images for each method. The complete list of prompts is included in the supplementary materials.
For all the tested methods, we considered the settings described in Section C.I including a classifier- free guidance scale of WCHO = 7.5, 50 reverse- diffus-ii steps, and the DPM solver. For the Particle Guide baseline, we used the following settings:
We applied the original implementation provided by the repository of [56] Since the method operates repeated generations of the same prompt, generated five samples per prompt using seeds 0 through 4. The coefficient parameter was set to 30, following the original implementation.
Particle Guide.
Gaussian Mixtures. We used conditional diffusion models in Figure 4
In Figure 7 we illustrate how the centers of clusters were used inputs the diffusion model simulate conditional generation.
D Additional Numerical Results
In this section, we provide additional numerical results for the SPARKE guidance method.
Ablation studies on the kernel function choice in SPARKE. In Figure we compared the outputs of applying SPARKE with the cosine similarity kernel and the Gaussian kernel in the latent space of
22

---

Stable Diffusion XL
= 0.0
SDXL+SPARKE Guidance (Ours)
0.01
Increase in SPARKE Guidance
17 = 0.03
17 0.05
17 0.07
1n 0.09
Prompt: A person standing next to the water and an umbrella.
Prompt: A man sits at table in front of a plate of food.
Figure 8: Qualitative results for various diversity guidance scales from = 0 (no guidance) to 7 0.09. The results are generated using Stable Diffusion XL with the same Gaussian kernel.
SDXL. As shown in the figure, the Gaussian kernel seems able to exhibit more diverse features, and therefore, the diversity of its images looks higher than the outputs of the cosine similarity kernel.
Hyperparameter selection for SPARKE. In Figure 8 we analyzed the impact of different diversity guidance scales Y), ranging from 0.09. This range was explored investigate the trade-off between generation quality and diversity. We observed that as gradually increased, there was corresponding increase in image diversity and a relative decrease in image quality. As a result, we chose 0.03 in experiments to show the balanced trade-off.
Effect of Classifier-Free Guidance scale on SPARKE guidanee. We study the Classifier-free guidance's impact on SPARKE for the Stable Diffusion 1.5 model, demonstrating how our method alleviates the known
while using the same setting of SD 1.5 as mentioned in Section C.2 We evaluated SPARKE's s effect on the
diversity trade-off [52]. We changed the CFG scale from
quality-diversity trade-off using Precision/Recall metrics in Figure 12 and Density/Coverage metrics in Figure [1 Our results show that SPARKE guidance maintains diversity in high CFG scale while preserving acceptable generation quality. Additionally, the Vendi score and Kernel Distance (KD) evaluations in Figure 10 show the same trend. Qualitative comparisons of generated samples at CFG
23

---

Gaussian Kernel
Cosine Kernel
Prompt A dog standing lying in front of crackling fireplace in chalet in Europe.
Prompt: A man casually drinking hot cup of coffee.
Prompt: A cat resting quietly on wooden chair.
Prompt: À dog standing beside cherry blossom tree in full bloom in East Asia.
Prompt: doctor wearing white coat a clinic.
Prompt: A dog standing guarding the entrance of historic palace in East Asia.
Figure 9: Qualitative comparison between SPARKE numerical results applying Gaussian (RBF) kernel and Cosine similarity kernel on Stable Diffusion XL.
scales w 4, 6, are presented in Figure 13 demonstrating that SPARKE produces diverse outputs without compromising quality.
Additional quantitative comparison with the baseline diversity-guided diffusion-based sample generations. Similar to Table we compare different guidance methods on Stable Diffusion 1.5 [60] in T
Latent space vs. ambient space. We compared latent-space guidance (as in SPARKE) with the
CLIP-embedded ambient-space guidance in c-VSG [I0] using three categories from the Ge
dataset (66) and modified with GPT-4o (74.. We use similar prompt template as mentioned in Table 7 in [10] add more details to the prompt. We provide additional samples in Figure 14 We

---

DIT XL 2:256
80-
XL 250
1.0
SPAAKK (Uhrr)
SPARKE (UheS)
KDDINOv 4
Vendi Score t
70-
0.6
50-
0.4
40-
0.2
CFG Weight
CFG Weight
Figure 10: Comparison of image generation diversity and quality in the DiT-XIL-2-256 model, analyzing the impact of SPARKE guidance through Vendi Score and Kernel Distance.
0.975
1.
DIT-X1-2-256
0.950
SPARKE (Ches)
Density t
144
0.925
Coverage
0.900
1.3
0.875
0.850
DIT-XL-2-256
0.825
SPARKE (Ohns)
2
CFG Weight
CFG Weight
Figure 11: Comparison of image generation quality and diversity in the DiT-XL-2-256 model, analyzing the impact of SPARKE guidance through density and coverage metrics.
also provide quantitative results in Table that although CL.IP-based Vendi scores were slightly higher for CLIP -ebeedddd ambient guidance, which could be due to optimizing Vendi with the CLIP features, the DINOv2-basee Vendi scores and in-batch similarity scores indicate higher diversity for the latent Vendi entropy guidance that we proposed for LDMs. Furthermore, latent guidance can be performed with considerably lower GPU memory (in our implementation 220GB for the latent case vs. approz35 GB for the ambient case), resulting in higher computational efficiency.
We use the following template:
Prompt to GPT-4o: "You are expert prompt optimizer for text-to-image models. Text-to-image models take a text prompt as input and generate images depicting the prompt as output. You translate prompts written by humans into better prompts for the text-to-image models. Your answers should be concise and effective. Your task is to optimize this prompt template written by human: "object in region". This prompt template used generate many images of objects such dogs, chairs, and cars in regions such as Africa, Europe, and East Asia. Generate one sentence of the initial prompt templates that contains the keywords "object" and "region" but increases the diversity of the objects depicted in the image."
Additional qualitative comparisons of vanilla, baseline diversity guided, and SPARKE prompt- aware diversity guided diffusion models. We compared the SPARKE prompt-aware diversity guidance method with ofate-of-the-art conditional latent diffusion models, including Stable Diffusion 2.1, Stable Diffusion XI. [ and PixArt-E [6].
Additional qualitative comparisons between prompt-aware (conditional RKE score) and prompt- unaware (RKE score) diversity guidance methods are presented on SD 2.1 (Figure [5]. Building on these observations, our results demonstrate that SPARKE improves prompt-aware diversity more effectively than grompt-unaware RKE guidance, as quantified by In-batch Similarity [56].
Furthermore, we showed additional results applied to PixArt- E (Figure [6) and Stable Diffusion XL (Figure 17) The qualitative comparison of SPARKE and without guidance shows SPARKE guidance significantly improves prompt-aware diversity relative to the baseline, highlighting its efficacy across varied latent diffusion model architectures.
ThhThh
25

---

XL
0.7
SPARKE (CwN))
Precision t
0.98
Recall +
0.5
0.97
04
0.3
SPARKE (Ours)
0.2
2
CFG Weight
CFG Weight
Figure 12: Comparison of image generation quality and diversity in the DiT-XIL-2-256 model, analyzing the impact of SPARKE guidance through precision and recall metrics.
Table 4: Quantitative comparison of guidance methods on Stable Diffusion 1.5 (Table 2 in the main text, extended SD 1.5).
Method
CLIPScore
KDx10
AuthPet t Cond- Vendi
Vendi t
In-batch Sim. 10a
SD v1.5
60
30.15
1.045
73.86
25.41
350.28
81.25
c-VSG 10
27.80
1.078
74.92
26.78
357.39
79.71
CADS 14
28.94
1.099
75.44
27.60
360.99
78.23
Particle Guide
(5
29.50
1.056
72.58
27.24
345.50
79.50
latent RKE (Ours)
29.23
1.081
78.02
28.75
369.50
78.30
SPARKE (Ours)
29.31
1.071
80.92
31.44
386.42
76.67
Table 5: Comparison of diversity metrics between (CLIP-embedded) ambient and latent guidance.
Guidance Method
IS 1
Vendi Score CLI
Vendi Score
In-batch Sim.
(eLledembedded) Ambient VSG 10
5.45
5.34
13.33
0.28
Latent VSG
7.24
4.42
25.22
0.15
26

---

DiT-XL-2 Model
DiT-XL-2 + SPARKE (Ours)
CFG Weight
CFG Weight
CFG Weight 8
Figure 13: Qualitative comparison of DiT-XL-2 with different classifier free guidance scales: (Left
side) standard DiT-XL-2 (Right side) DIT-XL-2 with SPARKE prompt-aware diversity guidance.
27

---

latent Vendi Score Guidance
CLIP-(Ambient) Vendi Score Guidance (c- (SVS
Prompt: A dog standing beside village hut in Kenya in Africa.
Prompt: A dog standing chasing birds along cobblestone street in Europe.
Prompt: A dog standing beside grand Gothic cathedral in Europe.
Prompt: A dog standing beside cherry blossom tree in full bloom in East Asia.
Prompt: A dog standing guarding a livestock enclosure in Africa.
Figure 14: Comparison of latent entropy guidance vs. CLIP-(ambient) entropy guidance on SD-XL. Additional Samples for Figure 2
28

---

Stable Diffusion 2.1
SPARKE: Prompt-Aware Diversity Guidance (Conditional RKE score)
Prompt-Unawars Diversity Guidance
(RKE score) In-batch Sim.: 79.01
In-batch Sim. 75.68
Prompts: (1) iter #6219: This image bench overlooking beach, iter #6537: white bench sitting that overlooks (3) #9353.A white wooden bench sitling lop green hill
Prompts: (1) iter #1300: bird branch on the ground, (2) iter #1375: A cute little bird standing some rocks, (3) iter #3234: A small bird standing top rock near grass.
Prompts: (1) iter 4242: Two dogs are looking while they stand near the toilet in the bathroom, (2) iter #3475: Two small dogs standing in restroom next to tuilet, (3) iter #4875: Small dogs standing in restruom next to a toilet.
Prompts: (1) iter #6365: A wooden bench with snow forest, (2) iter #7348: wood bench is outside covered snow, (3) iter #9237: A winter scene of park bench covered snow among the trees
Prompts: iter plate an orange some bar, orange snacks,
an
orange, chocolate, cracker, piece lettuce on plate
Prompt:: iter 48034: A person wearing winter gears skis down mountain, (2) iter #8527: woman hiking across a mountain with skis, (3) iter #9275: A man on ski's is standing the snow.
Figure 15: Comparison of SPARKE prompt-aware diversity guidance via conditional-RKE score diveerity--nawen diversity guidance using the RKE score SD 2.1 text-to-image generation. Additional Samples for Figure 5
29

---

PixArt-E
PixArt-Z + SPARKE Guidance
Prompts: 1. A photo of man posing for portrait, 2. A portrait of male facing forward, An upper body portrait of man.
Prompts: I. relaxed sitting still chair, fluffy sitting calmly 3. peaceful top of simple chair.
Prompts: sitting calmly among branches, resting peacefully on twig. holding bird.
Prompts: old walking elderly strolling through a gentleman taking road.
Prompts: small coloring table, child sitting drawing piece paper, making drawing paper.
Prompis: sitting quietly and reading reading bench, reading book relaxed setting
Prompts: young holding apple, female holding apple smiling, showing apple with both hands.
Figure 16: Qualitative Comparison of samples generated by standard PixArt-E SPARKE diversity guided Pi
30

---

SDXL
SDXL + SPARKE Guidance
Prompts: photo man posing portrait, portrait young facing forward, upper body portrait
Prompts: cat sitting chair, fluffy sitting calmly on seat, A peaceful top simple
Prompts: sitting calmly among the branches, resting peacefully twig, holding bird.
Prompts: old down elderly strolling through old gentleman laking walk the road.
Prompts: 1. A small kid coloring on table, 2. child sitting and drawing on piece of paper, 3. A kid making drawing on paper.
Prompts: 1. man sitting quietly and reading book, 2. A man reading book on a bench, man reading book relaxed setting
Prompts: young holding apple, holding an apple and smiling, woman showing apple hands.
Figure 17: Qualitative Comparison of samples generated by standard Stable Diffusion XL SPARKE diversity guided Stable Diffusion XL.
31

---

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38


Reviews:
[{"review_id": "ZJxkehVm0A", "reviewer": "Reviewer_wxtJ", "summary": "This paper considered the problem of ensuring prompt-aware diversity when guiding diffusion models. The main idea is based on using the matrix-based Rényi entropy (RKE score), which measures the kernel-based similarity between a class of $n$ prompts and associated images. By using a gradient-based optimization approach, the authors designed an algorithm that only needs to compute the gradient of the conditional RKE score, which further reduced the computational cost from $O(n^3)$ to $O(n)$. Numerical experiments on various text-to-image diffusion models are provided to demonstrate the proposed method's effectiveness in terms of prompting the diversity of generated images.", "questions": "The reviewer is satisfied with the quality of the manuscript and has just one follow-up question. Specifically, the authors of [10] have made a link between their proposed guidance method with other kernel-based/ensemble-based sampling methods like the Stein Variational Gradient Descent (SVGD) [11]. Would it be possible for the authors to briefly comment on how the method proposed in this manuscript may relate to other ensemble-based/kernel-based sampling methods in literature? (maybe like that of [12,13] - Is there a gradient-flow based interpretation of the proposed method?) Alternatively, would it be possible for the authors to provide some insights on how one may perform theoretical analysis (like that of [14,15,16]) on the proposed guidance methods, maybe at least for the case of Gaussian mixtures?", "limitations": "The reviewer is satisfied with the limitations that the authors briefly discussed at the end of the manuscript. Specifically, the authors mentioned that currently the methodology can only be used for image-based diffusion models. Hence, one of the future directions is to investigate whether the methodology can be generalized to other modalities like video and text.\n\nReferences:\n\n[1] Singhal, R., Horvitz, Z., Teehan, R., Ren, M., Yu, Z., McKeown, K., & Ranganath, R. (2025). A general framework for inference-time scaling and steering of diffusion models. arXiv preprint arXiv:2501.06848.\n\n[2] Chen, H., Ren, Y., Min, M. R., Ying, L., & Izzo, Z. (2025). Solving inverse problems via diffusion-based priors: An approximation-free ensemble sampling approach. arXiv preprint arXiv:2506.03979.\n\n[3] Skreta, M., Akhound-Sadegh, T., Ohanesian, V., Bondesan, R., Aspuru-Guzik, A., Doucet, A., ... & Neklyudov, K. (2025). Feynman-kac correctors in diffusion: Annealing, guidance, and product of experts. arXiv preprint arXiv:2503.02819.\n\n[4] Wu, L., Trippe, B., Naesseth, C., Blei, D., & Cunningham, J. P. (2023). Practical and asymptotically exact conditional sampling in diffusion models. Advances in Neural Information Processing Systems (NeurIPS), 36, 31372-31403.\n\n[5] Trippe, B. L., Yim, J., Tischer, D., Baker, D., Broderick, T., Barzilay, R., & Jaakkola, T. (2022). Diffusion probabilistic modeling of protein backbones in 3d for the motif-scaffolding problem. In The Eleventh International Conference on Learning Representations (ICLR), 2023.\n\n[6] Cardoso, G., Idrissi, Y. J. E., Corff, S. L., & Moulines, E. (2023). Monte Carlo guided diffusion for Bayesian linear inverse problems. In The Twelfth International Conference on Learning Representations (ICLR), 2024.\n\n[7] Dou, Z., & Song, Y. (2024). Diffusion posterior sampling for linear inverse problem solving: A filtering perspective. In The Twelfth International Conference on Learning Representations (ICLR), 2024.\n\n[8] Kim, S., M. Kim, and D. Park (2025). Test-time alignment of diffusion models without reward over-optimization. In The Thirteenth International Conference on Learning Representations (ICLR), 2025.\n\n[9] Guo, Y., Yuan, H., Yang, Y., Chen, M., & Wang, M. (2024). Gradient guidance for diffusion models: An optimization perspective. arXiv preprint arXiv:2404.14743.\n\n[10] Corso, G., Xu, Y., De Bortoli, V., Barzilay, R., & Jaakkola, T. (2023). Particle guidance: non-iid diverse sampling with diffusion models. In The Twelfth International Conference on Learning Representations (ICLR), 2024.\n\n[11] Liu, Q., & Wang, D. (2016). Stein variational gradient descent: A general purpose bayesian inference algorithm. Advances in Neural Information Processing Systems (NeurIPS), 29.\n\n[12] Wild, V. D., Ghalebikesabi, S., Sejdinovic, D., & Knoblauch, J. (2023). A rigorous link between deep ensembles and (variational) Bayesian methods. Advances in Neural Information Processing Systems (NeurIPS), 36, 39782-39811.\n\n[13] Li, L., Liu, Q., Korba, A., Yurochkin, M., & Solomon, J. (2022). Sampling with mollified interaction energy descent. In The Eleventh International Conference on Learning Representations (ICLR), 2023.\n\n[14] Chidambaram, M., Gatmiry, K., Chen, S., Lee, H., & Lu, J. (2024). What does guidance do? a fine-grained analysis in a simple setting. Advances in Neural Information Processing Systems (NeurIPS), 37.\n\n[15] Wu, Y., Chen, M., Li, Z., Wang, M., & Wei, Y. (2024). Theoretical insights for diffusion guidance: A case study for gaussian mixture models. International Conference on Machine Learning (ICML), PMLR, 2024.\n\n[16] Li, G., & Jiao, Y. (2025). Provable Efficiency of Guidance in Diffusion Models for General Data Distribution. arXiv preprint arXiv:2505.01382.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Pros: The reviewer finds that the paper is presented in a clear way for the readers to comprehend. For all theoretical arguments, the authors have included detailed proof in the appendix. Also, several large-scale models like Stable Diffusion are used to test the validity of the proposed method. Both experimental and implementational details are provided. \n\nCons: The reviewer found no significant weaknesses of the paper. However, the authors are encouraged to perform a more comprehensive literature review for related work on guidance. For instance, to the best of the reviewer's knowledge, a popular class of work have developed guidance methods based on sequential monte carlo (SMC), such as [1,2,3,4,5,6,7,8] (Though some work might have studied different problems like inference-time scaling or Bayesian inverse problems, the formulation is similar). Other work that the authors might have missed citing include [9], which discusses an optimization based formulation of guidance methods.", "was_revised": true, "final_justification": "The reviewer has checked all of the reviews and the authors' responses. Overall, most issues related to both theoretical and practical aspects of the proposed method have been resolved. Therefore, given that the additional experimental results attached in the authors' rebuttal haven't been added to the main text yet, the reviewer is recommending \"Borderline Accept\" by maintaining a score of 4.", "rebuttal": "We would like to thank Reviewer wxtJ for the constructive and thoughtful feedback and are delighted to hear that the reviewer found our work “clearly presented” and “well-supported by theoretical proofs and large-scale experiments”. Below is our response and clarifications regarding the questions and comments in the review:\n\n**1- Literature review for related works on guidance**\n\nWe thank Reviewer wxtJ for mentioning the related works on guidance in diffusion models. As pointed out in the review, a more comprehensive discussion of guidance methods, particularly those based on Sequential Monte Carlo (SMC) and optimization formulations, will definitely position our work better in this literature. We will revise the related work section to include and discuss the mentioned references.\n\n**2- Relation to other kernel-based sampling methods**\n\nWe thank the reviewer for the valuable feedback and for raising the connection to other kernel-based sampling methods. We appreciate this opportunity to clarify the theoretical distinctions and contributions of SPALE. \n\nOur answer to the reviewer’s question is positive, and there is a gradient-flow-based interpretation of our method. SPALE, along with Stein Variational Gradient Descent (SVGD)[1], Particle Guidance (PG)[2], and the ensemble-based/kernel-based sampling methods in [3, 4], can be understood as an interacting particle system that follows a gradient flow to minimize a specific energy function:\n$$\\mathrm{d}\\mathbf{z}^{(n)} = \\left[ - \\mathbf{f}(\\mathbf{z}^{(n)}, t') + \\frac{g^2(t')}{2} \\left( \\nabla_{\\mathbf{z}^{(n)}} \\log p_{t'}(\\mathbf{z}^{(n)}) - \\eta \\nabla_{\\mathbf{z}^{(n)}} L_{\\text{Cond-IRKE}}(\\mathbf{z}_1, \\dots, \\mathbf{z}_n) \\right) \\right] \\mathrm{d}t + g(t') \\mathrm{d}\\mathbf{w}$$\nWhile previous methods define a gradient flow to optimize for sample quality and **prompt-unaware** diversity, our proposed SPALE defines a flow to minimize a Conditional Inverse-Rényi Kernel Entropy (Cond-IRKE). The core idea of SPALE lies in the novelty of the energy function it minimizes, thus represents a forward by introducing *prompt-awareness* and improving *scalability*.\n\n**Prompt-Awareness**. Previous methods like Particle Guidance (PG)[10] employ a prompt-unaware repulsion mechanism. Their guidance potential $\\log \\Phi_{t'}(\\mathbf{z}_1, \\dots, \\mathbf{z}_n)$ treats all samples in a batch of different prompts equally, applying a uniform repulsion force between every pair regardless of their corresponding prompts. This uniform repulsion limits the computational efficiency, and it is not completely aligned with the goal of generating diverse outputs within related contexts, i.e., prompt categories. SPALE introduces a prompt-aware guidance mechanism, which is the key difference from previous methods. By optimizing the **Conditional Rényi Kernel Entropy** during sampling, our guidance potential is defined by:\n$$\n\\nabla\\_{z^{(n)}} L\\_{\\text{Cond-IRKE}} \\propto \\mathbb{E}\\_{ {(\\mathbf{z}', \\mathbf{y}') \\sim P\\_{n-1}} } \\left[ k\\_Z(\\mathbf{z}', \\mathbf{z}^{(n)}) \\cdot k\\_Y(\\mathbf{y}', \\mathbf{y}^{(n)}) \\nabla\\_{z^{(n)}} k\\_Z(\\mathbf{z}', \\mathbf{z}^{(n)}) \\right]\n$$\n \n**Linear-Time Computational Scalability**. We would like to clarify that in studying the scalability of the proposed SPALE method, we specifically compare it with other diversity-score-based guidance methods, including the Vendi score guidance. The computation of the Vendi score and its gradient requires $O(n^3)$ computations for $n$ generated samples, which enforces considering short windows for applying the diversity guidance in generating a moderately large number of data. On the other hand, the proposed SPALE method switches to the RKE score whose gradient can be calculated with $O(n)$ computations, which allows us to scale the diversity score-guided sample generation to several thousands. We would like to highlight that as shown Theorem 1 in [5], the RKE (entropy order-2) is the only entropy score with such a property in the family of Renyi entropy measures. We will make this point on the scalability of SPALE in comparison to the Vendi score diversity guidance clear.   \n\n**3- Insights of theoretical analysis of RKE Guidance**\n\nAs previously discussed, our guidance algorithm follows the gradient-flow-based sampling formulations, and we provide a theoretical insight into interpreting how Rényi Kernel Entropy (RKE) score[6] and Conditional RKE score[7] enhance the sample diversity. \n\nThe main insight is that the order-2 RKE score serves as a differentiable objective for counting the modes of a particle distribution, and [6] provides a theoretical analysis about the RKE score of the kernel covariance matrix of mixtures of Gaussian and sub-Gaussian components. Furthermore, the Conditional RKE score in [7] quantifies the internal diversity conditioning on the prompt categories. \n\nSPALE defines a gradient flow that optimizes the Conditional RKE score. This process sequentially drives samples to cover distinct modes, while the conditional mechanism ensures the prompt-aware diversity guidance potential. The dynamic nature of this sequential generation scheme makes it analytically challenging to characterize the final joint distribution of the samples. In the revised version, we will include the above discussion on how SPALE achieves prompt-aware diversity via RKE score and Conditional RKE score for future analysis.\n\n---\n\n[1] Liu, Q., & Wang, D. (2016). Stein variational gradient descent: A general purpose bayesian inference algorithm. Advances in neural information processing systems, 29.\n\n[2] Corso, G., Xu, Y., De Bortoli, V., Barzilay, R., & Jaakkola, T. S. Particle Guidance: non-IID Diverse Sampling with Diffusion Models. In The Twelfth International Conference on Learning Representations.\n\n[3] Wild, V. D., Ghalebikesabi, S., Sejdinovic, D., & Knoblauch, J. (2023). A rigorous link between deep ensembles and (variational) bayesian methods. Advances in Neural Information Processing Systems, 36, 39782-39811.\n\n[4] Li, L., Korba, A., Yurochkin, M., & Solomon, J. Sampling with Mollified Interaction Energy Descent. In The Eleventh International Conference on Learning Representations.\n\n[5] Ospanov, A., & Farnia, F. Do Vendi Scores Converge with Finite Samples? Truncated Vendi Score for Finite-Sample Convergence Guarantees. In The 41st Conference on Uncertainty in Artificial Intelligence.\n\n[6] Jalali, M., Li, C. T., & Farnia, F. (2023). An information-theoretic evaluation of generative models in learning multi-modal distributions. Advances in Neural Information Processing Systems, 36, 9931-9943.\n\n[7] Jalali, M., Ospanov, A., Gohari, A., & Farnia, F. (2024). Conditional Vendi Score: An information-theoretic approach to diversity evaluation of prompt-based generative models. arXiv preprint arXiv:2411.02817."}, {"review_id": "EoGYGVhOdB", "reviewer": "Reviewer_HGHP", "summary": "This paper proposes a novel method named SPALE (Scalable Prompt-Aware Latent Entropy-based Diversity Guidance) to address the issue of insufficient diversity in generated samples from prompt-guided diffusion models. The core idea is to introduce a \"prompt-aware\" diversity guidance mechanism, enabling diversity optimization to dynamically adjust based on the semantic similarity between input prompts.", "questions": "See Weaknesses.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1. Achieving \"meaningful\" diversity in prompt-guided generative models is a very practical and critical challenge in this field. Simply increasing the dissimilarity of all samples without considering the similarity of the prompts may harm the alignment between the generated results and the prompts. This work clearly articulates the necessity of \"prompt-aware\" diversity;\n2. Rigorous and Comprehensive Experiments: Multiple representative state-of-the-art diversity-enhancing methods, such as c-VSG, CADS, and Particle Guidance, were selected as baseline methods, with extensive ablation experiments and evaluations conducted;\n3. The paper is overall Clear and Well-written.\n\n**Weaknesses**\n1. This method introduces a key hyperparameter - diversity-guided scale η. Although the setting of the parameter may be mentioned in the appendix, there is a lack of analysis on the sensitivity of this parameter in the main text.\n2. The paper shows fewer examples of qualitative comparison, and the generated images have obvious artifacts. Will this method sacrifice some image quality?", "was_revised": true, "final_justification": "Thanks to the replies and additional experiments from the authors, most of my concerns have been resolved. However, I still feel that there is room for improvement regarding the performance and general applicability of the proposed method. I will provide my final rating after considering the opinions of the other reviewers.", "rebuttal": "We would like to thank Reviewer HGHP for the thoughtful feedback on our work. We are glad that the reviewer finds our experiments “rigorous and comprehensive” and the paper “clear and well-written”. Below is our response and clarifications regarding the questions and comments in the review:\n\n**1- Analysis on diversity guidance scale $\\eta$**\n\nWe appreciate the reviewer’s point on the diversity guidance scale hyperparameter. We would like to kindly refer the reviewer to Figure 6 in the appendix in the supplementary material, where we qualitatively compared the effect of the guidance scale ranging from 0 to 0.1 on the prompt-guided sample generation using SDXL.\n\nTo further address the reviewer’s comment, in the following table, we provide a quantitative comparison of the performance with different $\\eta$ values on class conditional Diffusion Transformer (DiT-XL/2), which shows the higher diversity of the generated data with larger values of $\\eta$ with only a minor reduction in the Precision/Density in sample generation. Specifically, our numerical results highlight that with a choice of $\\eta$ in the range of $[0.02, 0.06]$, the diversity score can significantly grow while preserving the Precision/Density of generated data. In the revision, we will include Figure 6 and the following table in the main text.\n\n| Diversity Scale ($\\eta$) | Precision $\\uparrow$ | Recall $\\uparrow$ | Density $\\uparrow$ | Coverage $\\uparrow$ |\n|------------------------|-----------|--------|---------|----------|\n| **0 (No Guidance)**        | 0.946     | 0.136  | 1.358   | 0.561    |\n| **0.02**                   | 0.944     | 0.231  | 1.345   | 0.682    |\n| **0.04**                   | 0.967     | 0.259  | 1.352   | 0.776    |\n| **0.06**                   | 0.955     | 0.264  | 1.349   | 0.781    |\n| **0.08**                   | 0.941     | 0.357  | 1.329   | 0.796    |\n| **0.1**                    | 0.923     | 0.361  | 1.326   | 0.798    |\n\n**2- Qualitative comparison of SPALE guidance**\n\nRegarding this comment, we would like to refer the reviewer to kindly view the randomly selected samples from different diffusion models in Figure 11 (Qualitative results with different CFG scales), Figure 14 (PixArt-$\\Sigma$ results), and Figure 15 (SDXL results) in the appendix.\n\nTo further address the reviewer’s comment, we also provide quantitative comparisons of these state-of-the-art models, as shown in the following table, which shows an increase in diversity scores (Con-Vendi, Vendi, In-batch Sim, scores) with only a minor decrease in the evaluated CLIPScore. We also highlight that the kernel distance (KD) evaluation score (evaluating both quality and diversity) and the Authenticity score (with MS-COCO being the reference dataset) have indeed improved in the guided sample generation, indicating that the scores evaluating both quality and diversity have increased. \n\n| Method                  | CLIPScore $\\uparrow$ | KD $\\times 10^2 \\downarrow$ | AuthPct $\\uparrow$ | Cond-Vendi Score $\\uparrow$  | Vendi Score $\\uparrow$ | In-batch Sim.$\\times 10^2 \\downarrow$ |\n|-------------------------|----------------------|------------------|---------|------------------|-------------|----------------------------|\n| **SDXL**                    | 31.17                | 66.37            | 76.28   |        27.54     |   309.54    | 81.67                      |\n| **SDXL + SPALE**            | 30.47                | 62.62            | 80.92   |          31.17   |   313.80    | 77.75                      |\n| **PixArt-$\\Sigma$**         | 31.01                | 65.37            | 78.13   |       26.45      |   307.36    | 83.84                      |\n| **PixArt-$\\Sigma$ + SPALE** | 30.66                | 63.86            | 81.48   |       32.14      |   322.25    | 78.81                      |\n\n\n**3- Qualitative comparison of Latent (ours) vs Ambient-based diversity guidance methods**\n\nWe would like to highlight that one key property of our proposal is that we apply guidance on the latent space in contrast to the previous works that guide diversity scores in the ambient space (after passing through the CLIP or DINO embeddings). We observed that in large-scale diffusion models, the latent diversity guidance prevents generation artifacts and will generate semantically diverse concepts. In Figure 3 (in the main text), we showed the comparison of Vendi score guidance on the latent space vs. CLIP ambient space on SDXL, which shows that ambient guidance will lead to noticeable noise in the image, rather than true semantic diversity. Additional qualitative results are provided in Figure 12 of the Appendix, which further support this point."}, {"review_id": "Dgk8hNtysO", "reviewer": "Reviewer_THSZ", "summary": "This submission aims to enhance the diversity of results generated by text-to-image diffusion models. It introduces a conditional entropy-based guidance mechanism to improve image diversity. To reduce computational cost, the method approximates conditional entropy using the RKE score. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed approach.", "questions": "My major concern lies in the lack of experimental evaluations. It is unclear to me how the proposed method works in more practical settings and whether it will hurt generation quality.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n- the proposed method is new and has solid theoretical foundation. \n- the paper is written well and easy to follow.\n\n\nWeakness:\n- The main weakness is the limited experimental evaluation. The method is only evaluated on MSCOCO 1000 prompts. It is unclear how its generalization ability to generating more diverse images. \n\n- It is unclear whether the proposed method hurts quality of the generated images. From Table 2, the CLIP score is lower than SD (no guidance), even if the proposed method is using CFG. \n\n- Is the diversity score calculation reliable at early diffusion steps?", "was_revised": true, "final_justification": "Thanks for the authors response. Most of my concerns are addressed. I will keep the positive rating.", "rebuttal": "We would like to thank Reviewer THSZ for the thoughtful feedback and are glad that the reviewer found our method to be “new” and with “solid theoretical foundation”. Below is our response and clarifications regarding the questions and comments in the review:\n\n**1- Number of Prompts in the Numerical Evaluation**\n\nFirst, we think there might be a misunderstanding of the number of MS-COCO prompts in our experiments; The actual number is 10,000, which is stated to be only 1000 in the reviewer’s comment.  \n\nTo further investigate this, we have numerically validated that the diversity represented by the selected 10,000 MSCOCO prompts can reflect the diversity of the entire MS-COCO validation set. To do this, we measured the Recall [1] and Coverage [2] scores of the selected prompts with respect to the reference set of the whole MSCOCO validation set: The Recall score was 0.91, and the Coverage score was 0.96, suggesting that a major fraction of the prompt clusters in MSCOCO are present in the selected set.   \n\n**2- Quantitative evaluation on additional diffusion models**\n\nTo address the reviewer's comment, we provide the quantitative evaluation results on the state-of-the-art text-to-image diffusion models, SDXL and PixArt-$\\Sigma$, in the following table. The numerical results indicate a similar trend to the Stable diffusion cases in Table 2 of the main text.\n\n| Method                  | CLIPScore $\\uparrow$ | KD $\\times 10^2 \\downarrow$ | AuthPct $\\uparrow$ | Cond-Vendi Score $\\uparrow$  | Vendi Score $\\uparrow$ | In-batch Sim.$\\times 10^2 \\downarrow$ |\n|-------------------------|----------------------|------------------|---------|------------------|-------------|----------------------------|\n| **SDXL**                    | 31.17                | 66.37            | 76.28   |        27.54     |   309.54    | 81.67                      |\n| **SDXL + SPALE**            | 30.47                | 62.62            | 80.92   |          31.17   |   313.80    | 77.75                      |\n| **PixArt-$\\Sigma$**         | 31.01                | 65.37            | 78.13   |       26.45      |   307.36    | 83.84                      |\n| **PixArt-$\\Sigma$ + SPALE** | 30.66                | 63.86            | 81.48   |       32.14      |   322.25    | 78.81                      |\n\n\n**3- Quality and Diversity trade-off in the SPALE guidance**\n\nRegarding this comment, we would like to refer to the Appendix, Figure 11 (Qualitative results with different CFG scales) and Figures 8, 9, and 10 for a quantitative comparison of the quality/diversity trade-off with precision/recall, density/coverage, and Vendi Score/KD. Furthermore, we have included randomly selected samples generated by the PixArt-$\\Sigma$ and SDXL diffusion models in Figure 14 (PixArt-$\\Sigma$ results) and Figure 15 (SDXL results) in the appendix.\n\nAlso, we would like to highlight that CLIP-Score may not fully reflect the semantic alignment of a text and image pair in the presence of multiple components in the input image. As noted in Reference [3] (refer to Figure 1 in this paper), the image encoder of CLIP could favor larger objects, while its text encoder could prioritize first-mentioned objects. Similarly, Reference [4] states that “CLIP puts a large focus on the few main objects of an image”. Such biases in the CLIP embedding may potentially lead to slightly lower CLIP-Scores when diverse components are also present in the image.\n \n\n**4- Reliability of the score in early diffusion steps**\n\nWe thank the reviewer for pointing this out. We would like to highlight that one advantage of applying guidance in the latent space, rather than in the ambient space, is that it does not require the latent representation to be decoded into an image, which can be especially useful in early diffusion steps. This feature of latent RKE diversity guidance avoids the need for computing scores on noisy intermediate images during the early diffusion steps, which might lead to unreliable evaluated scores.\n\n---\n\n[1] Kynkäänniemi et al. Improved Precision and Recall Metric for Assessing Generative Models. In NeurIPS 2019\n\n[2] Naeem et al. Reliable Fidelity and Diversity Metrics for Generative Models. In ICML 2020\n\n[3] Abbasi et al., CLIP Under the Microscope: A Fine-Grained Analysis of Multi-Object Representation. In CVPR 2025\n\n[4] Stein et al. Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models.In NeurIPS 2023"}, {"review_id": "KwPol9gctk", "reviewer": "Reviewer_W1na", "summary": "The authors present SPALE, a training-free method that drives text-to-image diffusion models toward more diverse outputs. SPALE injects an order 2 RKE term straight into the model’s latent space. Because the order 2 form replaces the eigen decomposition used by Vendi-score guidance with simple Frobenius-norm calculations, every sampling step falls from cubic to roughly linear time and shrinks GPU memory needs. A second kernel, computed between prompt embeddings, gates the entropy so that images arising from semantically similar prompts repel one another, removing the brittle pre-clustering step found in earlier prompt-aware approaches.\n\nExperiments on SD 2.1 and SDXL show that SPALE raises Vendi-score, coverage, and conditional Vendi-score by up to twenty percent while keeping inception score, CLIPScore, and authenticity nearly unchanged. Compared with CLIP-based ambient guidance and CADS, SPALE cuts peak memory, stays stable, and yields lower in-batch similarity within each prompt group, confirming stronger within-prompt diversity. The paper also reports synthetic 2D tests that back the analytical claim.", "questions": "N/A.", "limitations": "N/A.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper presents a careful mathematical derivation that replaces the Vendi-score eigen-decomposition with an order 2 RKE term whose gradient is both easier to compute and cheaper in memory, reducing the per-step complexity.\n2. The method is training-free and therefore simple to add to any diffusion sampler; the authors show that peak GPU memory drops a lot compared with CLIP-based guidance.\n3. Experiments demonstrate consistent gains in diversity metrics (Vendi-score, coverage, conditional Vendi-score) while inception score, CLIPScore, and authenticity remain virtually unchanged.\n4. An ablation study links each design choice—entropy order, prompt-similarity kernel, and kernel bandwidth—to changes in output, providing evidence that the improvements are due to the proposed components rather than uncontrolled factors.\n\n\nWeakness:\n1. The authors do not report the runtime of their approach in comparison with other baselines, so the practical benefit remains unclear.\n2. The qualitative comparison in Table 2 is limited to SD. Without the results for SDXL, it is unclear whether this method is only effective for SD or for diffusion methods in general.", "was_revised": true, "final_justification": "I think this is a good and interesting paper. The experiments show improvements on several backbones, and the method has good theoretical motivations.", "rebuttal": "We would like to thank Reviewer W1na for the thoughtful feedback and are glad that the reviewer found our paper to “present a careful mathematical derivation” and our numerical result to “demonstrate consistent gains in diversity metrics”. Below is our response and clarifications regarding the questions and comments in the review:\n\n\n**1- runtime comparison of SPALE guidance with the baselines**\n\nWe thank the reviewer for pointing this out. To address the comment, we evaluated SPALE's computational efficiency by comparing its runtime and peak memory with those of the baselines over 1000 text-to-image generations (512×512 resolution) using a 50-step diffusion process on an NVIDIA RTX 4090 (24GB VRAM). The results are in the following table, indicating that SPALE requires significantly lower runtime and less memory (as it functions in the latent space). We will include this table in the revised manuscript.\n\n| Model + Guidance method              | **Runtime per sample (s)**       | **GPU Memory Peak (GB)** |\n|--------------------------------------|-----------------------|--------------------------|\n| **Stable Diffusion v1.5**            | 1.620 $\\pm$ 0.265     | 3.178 $\\pm$ 0.001        |\n| **SD-1.5 + SPALE (Ours)**            | **1.752 $\\pm$ 0.287** | **3.230 $\\pm$ 0.025**    |\n| **SD-1.5 + c-VSG**                   | 3.079 $\\pm$ 0.296     | 8.665 $\\pm$ 0.116        |\n| **SD-1.5 + Particle Guide (Pixel)**  | 4.912 $\\pm$ 0.312     | 7.531 $\\pm$ 0.032        |\n| **SD-1.5 + Particle Guide (DINOv2)** | 9.102 $\\pm$ 0.271     | 20.133 $\\pm$ 0.038       |\n\n**2- Additional quantitative comparison on state-of-the-art diffusion models**\n\nFollowing the reviewer’s comment, we have performed additional numerical evaluation and  here provide quantitative comparisons of the state-of-the-art models, SD-XL and PixArt-$\\Sigma$, in the following table. These quantitative results show SPALE results in an increase in diversity scores (Con-Vendi, Vendi, In-batch Sim, scores) with only a minor decrease in the evaluated CLIPScore. We also note that the kernel distance (KD) evaluation score (evaluating both quality and diversity) and the Authenticity score (with MS-COCO being the reference dataset) have both improved in the guided sample generation.\n\n| Method                  | CLIPScore $\\uparrow$ | KD $\\times 10^2 \\downarrow$ | AuthPct $\\uparrow$ | Cond-Vendi Score $\\uparrow$  | Vendi Score $\\uparrow$ | In-batch Sim.$\\times 10^2 \\downarrow$ |\n|-------------------------|----------------------|------------------|---------|------------------|-------------|----------------------------|\n| **SDXL**                    | 31.17                | 66.37            | 76.28   |        27.54     |   309.54    | 81.67                      |\n| **SDXL + SPALE**            | 30.47                | 62.62            | 80.92   |          31.17   |   313.80    | 77.75                      |\n| **PixArt-$\\Sigma$**         | 31.01                | 65.37            | 78.13   |       26.45      |   307.36    | 83.84                      |\n| **PixArt-$\\Sigma$ + SPALE** | 30.66                | 63.86            | 81.48   |       32.14      |   322.25    | 78.81                      |"}]

Author rebuttal:

Meta-review: This paper introduces Scalable Prompt-Aware Latent Entropy-based Diversity Guidance for prompt-aware diversity guidance. Reviewers are satisfied with the writing of the paper, the theoretical rigor, and the performance of the proposed method. Most of the raised concerns are addressed during the rebuttal. In the end, all the reviewers recommend accept. Therefore, I'm recommending an accepetance and encourage the authors to keep improving the current submission based on the feedbacks from reviewers.
Decision: Accept (poster)