CARE：面向扩散模型的条件感知表示正则化

# CARE: Condition-Aware Representation Regularization for Diffusion Models
Source: [https://arxiv.org/html/2609.28561](https://arxiv.org/html/2609.28561)
Fengjia GuoAffiliation:Department of Computer Science and Technology, Tsinghua University, Beijing, ChinaCorrespondence to:[guofj23@mails\.tsinghua\.edu\.cn](mailto:[email protected])Zhuoyi YangJie TangAffiliation:Department of Computer Science and Technology, Tsinghua University, Beijing, ChinaCorrespondence to:[jietang@tsinghua\.edu\.cn](mailto:[email protected])

###### Abstract

Recent advances in diffusion models highlight the importance of representation regularization for improving sample quality and training efficiency\. However, commonly used regularization methods often overlook the built\-in conditions \(such as labels or texts\) which directly determine the generation target\. In this work, we demonstrate how conditioning signals affect the feature distribution and introduce the CARE \(Condition\-Aware REpresentation regularization\)\. CARE is a lightweight plug\-and\-play regularization framework that dynamically modulates feature distribution based on condition similarity\. CARE leverages built\-in conditioning signals to judiciously guide the representation space, promoting tighter feature clusters for similar conditions without relying on explicit alignment losses or external supervision\. Empirically, CARE consistently improves both visual fidelity and convergence stability across both class\-to\-image and text\-to\-image tasks\. On ImageNet, CARE achieves a 19\.08% reduction in FID in 400k training steps, leading to a 3\.5×\\timesspeed\-up\. When applied to text\-to\-image generation, CARE lowers FID by 16\.61% in 200k iterations and improves semantic alignment between generated samples and text prompts\. Moreover, CARE can be seamlessly integrated with existing regularization methods, yielding additional performance gains\.

###### Keywords:

Diffusion Models, Image Generation, Representation Learning

††affiliationnotice:Equal contributionFigure 1:Overview of CARE\. Left: DiT pipeline\. Right: Representation and condition spaces with CARE regularization\. CARE penalizes representation collapse for all sample pairs, with a similarity\-dependent strength based on condition similarity\.Figure 2:FID\-50K on ImageNet 256×256 for SiT\-XL/2 with and without CARE\. All models are evaluated with SDE sampling, without CFG, using 250 sampling steps\. CARE consistently improves FID throughout training\.## 1Introduction

Diffusion and flow matching models\([Sohl\-Dickstein et al\., 2015](https://arxiv.org/html/2609.28561#bib.bib8);[Ho et al\., 2020](https://arxiv.org/html/2609.28561#bib.bib9);[Dhariwal and Nichol, 2021](https://arxiv.org/html/2609.28561#bib.bib18);[Lipman et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib19)\)have demonstrated remarkable generative capabilities across diverse modalities, including image\([Betker et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib15);[Esser et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib14)\), video\([Yang et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib12);[Wan et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib13)\), and 3D content\([Team, 2025](https://arxiv.org/html/2609.28561#bib.bib17)\)generation\. A widely held view is that representation learning is a key step in generative models training\. In particular, recent methods such as REPA\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)and dispersive loss\([Wang and He, 2025](https://arxiv.org/html/2609.28561#bib.bib3)\)have shown that explicitly regularizing internal representations—either by aligning them with vision foundation model\([Oquab et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib28)\)features or by encouraging feature dispersion from a contrastive perspective—can both accelerate convergence and improve sample quality\. However, these approaches do not make use of the semantic information combined with the image/video, such as labels or captions\.Can those conditions further improve the representation learning in diffusion?In this work, we give a positive answer via conditional\-aware regularization\.

To motivate our approach,[Figure3](https://arxiv.org/html/2609.28561#S1.F3)illustrates how alignment of intermediate representations with text conditions under linear probe evolves during diffusion training in text\-to\-image scenarios\. We observe a strong correlation between alignment and sample quality: as training progresses, representations become more aligned with their conditioning signals, accompanied by a consistent reduction in FID, suggesting that better\-structured, condition\-aware representation spaces lead to improved generative fidelity\.

Yet, existing representation regularizers neglect this conditional structure, leading to a mismatch between the learned feature space and the conditioning signals\. Consequently, samples conditioned on similar inputs may be undesirably scattered, degrading semantic consistency and controllability\.

To address this limitation, we introduceConditional\-Aware REpresentation Regularization \(CARE\), a simple yet effective plug\-and\-play loss that injects lightweight supervision into the representation learning objective\. Intuitively, CARE leverages semantic conditions to optimize the distribution of representations, requiring no external foundation models, and can be seamlessly combined with existing training objectives or other regularization methods\.

Figure 3:FID\-50K versus representation alignment with text conditions, measured by a linear probe on intermediate representations\. Across both settings with and without REPA, CARE consistently improves representation–condition alignment while reducing FID\.In summary, CARE is characterized by three key aspects:

- •An interpretable motivation\.CARE is motivated by an information\-theoretic interpretation of conditional representation regularization, providing an intuitive explanation of how condition similarity can be incorporated into representation dispersion\. This perspective is consistent with the Platonic Representation Hypothesis\([Huh et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib1)\), which suggests that representations across modalities tend to exhibit compatible geometric structures\.
- •Significant and complementary gains\.CARE consistently improves generation quality across across various conditioned generation tasks\. On ImageNet, a class\-to\-image benchmark, CARE consistently reduces the FID score compared to the baseline steps \(see[Figure2](https://arxiv.org/html/2609.28561#S0.F2)\)\. On text\-to\-image benchmarks, CARE yields a further 16\.61% reduction in FID\. Notably, CARE also maintains its benefits when combined with representation\-alignment techniques\.
- •Enhanced interpretability and structured representations\.Beyond performance gains, CARE provides enhanced interpretability of diffusion features\. As shown in[Figure3](https://arxiv.org/html/2609.28561#S1.F3), representations regularized by CARE show enhanced alignment with text conditions\.

## 2Related Work

### 2\.1Diffusion Models with Regularization

Recently, diffusion models\([Ho et al\., 2020](https://arxiv.org/html/2609.28561#bib.bib9);[Song et al\., 2020](https://arxiv.org/html/2609.28561#bib.bib10)\)have become a focal point of research interest due to their outstanding performance in image generation\([Rombach et al\., 2022](https://arxiv.org/html/2609.28561#bib.bib22);[Labs, 2024](https://arxiv.org/html/2609.28561#bib.bib16)\)\. Recent studies have revealed that explicitly regularizing internal representations of diffusion models can enhance both training efficiency and generation quality\. REPA\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)first introduces a feature alignment strategy, encouraging intermediate representations of diffusion models to align with those from powerful pretrained encoders\([Oquab et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib28)\)\. This alignment facilitates faster convergence and improves the semantic coherence of generated samples\.

Building upon this idea, several extensions have been proposed\. For instance, SARA\([Chen et al\., 2025b](https://arxiv.org/html/2609.28561#bib.bib6)\)and REG\([Wu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib5)\)further refine the feature alignment with structural and adversarial views or auxiliary tokens\. Meanwhile, dispersive loss\([Wang and He, 2025](https://arxiv.org/html/2609.28561#bib.bib3)\)approaches the problem from a contrastive learning perspective, encouraging feature dispersion to promote uniformity distribution of representations\.

### 2\.2Diffusion with Condition\-Integrated Objectives

Conventional approaches integrate conditioning only at the input level, such as by concatenating conditional embeddings with latent variables\([Rombach et al\., 2022](https://arxiv.org/html/2609.28561#bib.bib22)\)\. In contrast, recent studies seek to explicitly incorporate conditioning signals into the training objective and underlying distributions\. For example, CAR\-Flow\([Chen et al\., 2025a](https://arxiv.org/html/2609.28561#bib.bib29)\)introduces a conditional\-based reparameterization framework that adjusts both the source and target distributions in flow matching according to conditioning variables\. Similarly,[Issachar et al\. \(2025\)](https://arxiv.org/html/2609.28561#bib.bib30)proposes to design condition\-specific prior distributions for flow\-based generative models\.

These methods demonstrate the benefit of incorporating conditional structure directly into the training objective\. However, they primarily modify the underlying distributions, and require additional parameters \(as in\([Chen et al\., 2025a](https://arxiv.org/html/2609.28561#bib.bib29)\)\) or multi\-stage training \(as in\([Issachar et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib30)\)\)\.

In contrast, we focus on integrating conditional information into the representation space through a lightweight regularization term, without altering the diffusion process or requiring additional parameterization\.

## 3Method

### 3\.1Overview

Our goal is to improve the representation quality of conditional diffusion models by explicitly regularizing how features evolve under given conditions\. While recent works have shown that representation regularization benefits diffusion training, existing approaches are typically condition\-agnostic\. We proposeCondition\-Aware REpresentation Regularization \(CARE\), a plug\-and\-play objective that enforces condition\-aware dispersion of intermediate representations without relying on external encoders or additional computation\.

### 3\.2Preliminaries

Diffusion models\([Sohl\-Dickstein et al\., 2015](https://arxiv.org/html/2609.28561#bib.bib8);[Ho et al\., 2020](https://arxiv.org/html/2609.28561#bib.bib9);[Dhariwal and Nichol, 2021](https://arxiv.org/html/2609.28561#bib.bib18)\)learn to generate data by reversing a gradual noising process\. In the continuous\-time limit\([Song et al\., 2021](https://arxiv.org/html/2609.28561#bib.bib11)\), this process can be formulated as learning a probability flow that transports a simple priorp1​\(𝐱1\)=𝒩⁡\(0,I\)p\_\{1\}\(\\mathbf\{x\}\_\{1\}\)=\\mathcal\{N\}\(0,I\)toward the data distributionp0​\(𝐱0\)p\_\{0\}\(\\mathbf\{x\}\_\{0\}\)\.

Flow matching\([Lipman et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib19);[Liu et al\., 2023b](https://arxiv.org/html/2609.28561#bib.bib31)\)provides a unified framework for this learning process by directly predicting the conditioned velocity field𝐯θ​\(𝐱t,t,𝐜\)\\mathbf\{v\}\_\{\\theta\}\(\\mathbf\{x\}\_\{t\},t,\\mathbf\{c\}\)that satisfies

ℒFM=𝔼t,𝐱0,𝐱1​\[‖𝐯θ​\(𝐱t,t,𝐜\)−d​𝐱td​t‖22\],\\mathcal\{L\}\_\{\\text\{FM\}\}=\\mathbb\{E\}\_\{t,\\mathbf\{x\}\_\{0\},\\mathbf\{x\}\_\{1\}\}\\\!\\left\[\\left\\\|\\,\\mathbf\{v\}\_\{\\theta\}\(\\mathbf\{x\}\_\{t\},t,\\mathbf\{c\}\)\-\\frac\{\\mathrm\{d\}\\mathbf\{x\}\_\{t\}\}\{\\mathrm\{d\}t\}\\,\\right\\\|\_\{2\}^\{2\}\\right\],\(1\)where𝐱t=\(1−t\)​𝐱0\+t​𝐱1\\mathbf\{x\}\_\{t\}=\(1\-t\)\\mathbf\{x\}\_\{0\}\+t\\mathbf\{x\}\_\{1\}andd​𝐱td​t=𝐱1−𝐱0\\frac\{\\mathrm\{d\}\\mathbf\{x\}\_\{t\}\}\{\\mathrm\{d\}t\}=\\mathbf\{x\}\_\{1\}\-\\mathbf\{x\}\_\{0\}denotes the ground\-truth velocity under the data–noise coupling\. The conditioning variable𝐜\\mathbf\{c\}\(e\.g\., class label or text embedding\) guides the flow toward specific modes of the data distributionp0p\_\{0\}\.

### 3\.3CARE: Condition\-Aware REpresentation Regularization

Let𝐳θ​\(𝐱t,t,𝐜\)\\mathbf\{z\}\_\{\\theta\}\(\\mathbf\{x\}\_\{t\},t,\\mathbf\{c\}\)denote the intermediate representation at a given layer of a diffusion model\. Prior work\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)shows that the linear probing accuracy of such representations is positively correlated with sample quality\. We observe a similar phenomenon in text\-to\-image generation: as training progresses, representations become increasingly aligned with text conditions, accompanied by consistent improvements in generation quality \(see[Figure3](https://arxiv.org/html/2609.28561#S1.F3)\)\.

This observation resonates with the Platonic Representation Hypothesis\([Huh et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib1)\), which suggests that representations across different modalities tend to organize into compatible geometric structures\. From this perspective, conditioning signals \(e\.g\., class labels or text prompts\) and model representations can be viewed as inducing related structures in their respective spaces\. These observations motivate the desideratum that the representation space induced by𝐳θ\\mathbf\{z\}\_\{\\theta\}should preserve conditional structure, such that samples associated with semantically similar conditions exhibit more coherent geometric organization\.

Based on this motivation, we introduceCARE\(Condition\-Aware REpresentation regularization\), a lightweight auxiliary objective that explicitly incorporates condition similarity into representation regularization\. CARE does not impose hard constraints on representations; instead, it modulates the strength of repulsive regularization according to condition similarity, encouraging a condition\-aware organization of the representation space\. An intuitive interpretation of CARE and its connection to mutual\-information\-based objectives is provided in[AppendixA](https://arxiv.org/html/2609.28561#A1)\.

Concretely, we define two functionss⁡\(⋅,⋅\)s\(\\cdot,\\cdot\)andψ⁡\(⋅\)\\psi\(\\cdot\)\. The functions⁡\(⋅,⋅\)∈\[0,1\]s\(\\cdot,\\cdot\)\\in\[0,1\]measures the similarity between conditioning signals, while the decreasing functionψ⁡\(⋅\)\\psi\(\\cdot\)controls the degree to which condition similarity influences representation regularization\. Given a batch of representations and conditions\{\(𝐳i,𝐜i\)\}i=1N\\\{\(\\mathbf\{z\}\_\{i\},\\mathbf\{c\}\_\{i\}\)\\\}\_\{i=1\}^\{N\}, CARE is defined as

ℒCARE=𝔼i,j​\[log⁡\(∑i,jψ⁡\(s⁡\(𝐜i,𝐜j\)\)​ϕ​\(𝐳i,𝐳j\)\)\],\\mathcal\{L\}\_\{\\text\{CARE\}\}=\\mathbb\{E\}\_\{i,j\}\\\!\\left\[\\log\\left\(\\sum\_\{i,j\}\\psi\\\!\\left\(s\(\\mathbf\{c\}\_\{i\},\\mathbf\{c\}\_\{j\}\)\\right\)\\,\\phi\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\)\\right\)\\right\],\(2\)whereϕ⁡\(⋅,⋅\)\\phi\(\\cdot,\\cdot\)is a kernel function defined in the representation space\.

The final training objective augments the original diffusion objective with CARE:

ℒ=ℒFM\+λ​ℒCARE\.\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{FM\}\}\+\\lambda\\,\\mathcal\{L\}\_\{\\text\{CARE\}\}\.\(3\)

### 3\.4Instantiations

We set the kernelϕ\\phito be a Gaussian kernel,

ϕ\(𝐳i,𝐳j\)∝exp\(−∥𝐳i−𝐳j∥22/d\),\\phi\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\)\\propto\\exp\\\!\\left\(\-\\\|\\mathbf\{z\}\_\{i\}\-\\mathbf\{z\}\_\{j\}\\\|\_\{2\}^\{2\}/d\\right\),\(4\)whereddis the dimension of𝐳i,𝐳j\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\. The division byddprovides a simple normalization that stabilizes the kernel scale in high\-dimensional spaces\.

#### 3\.4\.1Class\-Conditional Diffusion

For class\-conditional generation,𝐜\\mathbf\{c\}is a discrete label, and the similarity function reduces tos\(𝐜i,𝐜j\)=𝟙\[𝐜i=𝐜j\]s\(\\mathbf\{c\}\_\{i\},\\mathbf\{c\}\_\{j\}\)=\\mathds\{1\}\[\\mathbf\{c\}\_\{i\}=\\mathbf\{c\}\_\{j\}\]\. We setψ⁡\(s\)=α∈\(0,1\)\\psi\(s\)=\\alpha\\in\\left\(0,1\\right\)ifs=1s=1andψ⁡\(s\)=1\\psi\(s\)=1otherwise\.

#### 3\.4\.2Feature\-Conditional Diffusion

For feature\-conditional diffusion \(e\.g\., text\-to\-image generation\), the condition𝐜\\mathbf\{c\}is a continuous embedding, such as a CLIP text feature or a control\-image feature\. We explore two alternative formulations ofs⁡\(⋅,⋅\)s\(\\cdot,\\cdot\):

##### \(1\) Linear cosine scaling\.

We first compute the cosine similarity and linearly rescale it to the range\[0,1\]\[0,1\]:

slinear​\(𝐜i,𝐜j\)=12​𝐜i⊤​𝐜j‖𝐜i‖​‖𝐜j‖\+12\.s\_\{\\text\{linear\}\}\(\\mathbf\{c\}\_\{i\},\\mathbf\{c\}\_\{j\}\)=\\frac\{1\}\{2\}\\frac\{\\mathbf\{c\}\_\{i\}^\{\\top\}\\mathbf\{c\}\_\{j\}\}\{\\\|\\mathbf\{c\}\_\{i\}\\\|\\\|\\mathbf\{c\}\_\{j\}\\\|\}\+\\frac\{1\}\{2\}\.\(5\)

##### \(2\) Softmax\-normalized similarity\.

Alternatively, we normalize similarities across the batch to emphasize relative relationships:

ssoftmax​\(𝐜i,𝐜j\)=exp⁡\(𝐜i⊤​𝐜j‖𝐜i‖​‖𝐜j‖/τc\)∑kexp⁡\(𝐜i⊤​𝐜k‖𝐜i‖​‖𝐜k‖/τc\),s\_\{\\text\{softmax\}\}\(\\mathbf\{c\}\_\{i\},\\mathbf\{c\}\_\{j\}\)=\\frac\{\\exp\\\!\\left\(\\frac\{\\mathbf\{c\}\_\{i\}^\{\\top\}\\mathbf\{c\}\_\{j\}\}\{\\\|\\mathbf\{c\}\_\{i\}\\\|\\\|\\mathbf\{c\}\_\{j\}\\\|\}/\\tau\_\{c\}\\right\)\}\{\\sum\_\{k\}\\exp\\\!\\left\(\\frac\{\\mathbf\{c\}\_\{i\}^\{\\top\}\\mathbf\{c\}\_\{k\}\}\{\\\|\\mathbf\{c\}\_\{i\}\\\|\\\|\\mathbf\{c\}\_\{k\}\\\|\}/\\tau\_\{c\}\\right\)\},\(6\)where the temperatureτc\>0\\tau\_\{c\}\>0controls the sharpness of the similarity distribution\.

For both formulations, we introduce a hyperparameterα\\alphainψ\\psito stay aligned with the formulation in class\-conditional setting\.

ψ⁡\(s\)=s⋅\(α−1\)\+1,0<α<1\.\\psi\(s\)=s\\cdot\(\\alpha\-1\)\+1,0<\\alpha<1\.\(7\)
Both formulations are compatible with the CARE regularization, but lead to different behaviors: the linear version is an*absolute*measurement of similarity, while the softmax version is a*relative*variant within batch\. We evaluate both in[Section4\.3\.2](https://arxiv.org/html/2609.28561#S4.SS3.SSS2)to analyze how the choice ofs⁡\(⋅,⋅\)s\(\\cdot,\\cdot\)affects conditional alignment\.

## 4Experiments

Table 1:CARE consistently improves diffusion models across class\-to\-image and text\-to\-image benchmarks\.MethodIter\.SamplerNFEsCFG scaleFID↓\\downarrowIS↑\\uparrowCLIP\-T↑\\uparrowclass\-to\-image generationSiT\-B/2400kSDE2501\.033\.0243\.71\-SiT\-B/2 \+ dispersive loss400kSDE2501\.031\.3747\.85\-SiT\-B/2 \+ CARE400kSDE2501\.029\.7150\.10\-SiT\-B/2 \+ REPA400kODE2501\.024\.3162\.23\-SiT\-B/2 \+ REPA \+ dispersive loss400kODE2501\.023\.3664\.79\-SiT\-B/2 \+ REPA \+ CARE400kODE2501\.021\.6468\.50\-SiT\-XL/2400kSDE2501\.017\.1976\.52\-SiT\-XL/2 \+ dispersive loss400kSDE2501\.015\.5781\.68\-SiT\-XL/2 \+ CARE400kSDE2501\.013\.9189\.84\-SiT\-XL/2\([Ma et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib20)\)7MSDE2501\.08\.26131\.65\-SiT\-XL/2 \+ CARE2\.4MSDE2501\.07\.97131\.16\-SiT\-XL/2400kSDE2501\.55\.36167\.75\-SiT\-XL/2 \+ dispersive loss400kSDE2501\.54\.74178\.81\-SiT\-XL/2 \+ CARE400kSDE2501\.54\.09193\.76\-SiT\-XL/2\([Ma et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib20)\)7MODE2501\.52\.13256\.58\-SiT\-XL/2 \+ CARE2\.4MODE2501\.52\.10258\.63\-SiT\-XL/2 \+ REPA400kODE2501\.08\.81119\.61\-SiT\-XL/2 \+ REPA \+ CARE400kODE2501\.08\.31125\.34\-text\-to\-image generationMMDiT200kODE502\.011\.32\-18\.25MMDiT \+ dispersive loss200kODE502\.09\.98\-18\.60MMDiT \+ CARE200kODE502\.09\.44\-18\.54MMDiT \+ REPA200kODE502\.08\.16\-19\.25MMDiT \+ REPA \+ dispersive loss200kODE502\.07\.80\-19\.60MMDiT \+ REPA \+ CARE200kODE502\.07\.44\-19\.66MMDiT300kODE502\.08\.77\-18\.92MMDiT \+ dispersive loss300kODE502\.07\.44\-19\.21MMDiT \+ CARE300kODE502\.07\.02\-19\.16### 4\.1Experiments Settings

Class Conditioned Image GenerationWe conduct experiments on the ImageNet dataset\([Deng et al\., 2009](https://arxiv.org/html/2609.28561#bib.bib21)\)at 256×\\times256 resolution for class\-to\-image generation\. Our experiments are conducted on standard SiT\([Ma et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib20)\)models\. We strictly follow the original implementations in\([Ma et al\., 2024](https://arxiv.org/html/2609.28561#bib.bib20)\)and train the models on the latent space produced by SD\-VAE\([Rombach et al\., 2022](https://arxiv.org/html/2609.28561#bib.bib22)\)\. Sampling is performed using the SDE Euler\-Maruyamasampler with 250 steps without classifier\-guidance \(CFG\)\([Ho and Salimans, 2022](https://arxiv.org/html/2609.28561#bib.bib23)\)by default\. For evaluations, we report Fréchet inception distance \(FID\([Heusel et al\., 2017](https://arxiv.org/html/2609.28561#bib.bib7)\)\) and inception score \(IS\([Salimans et al\., 2016](https://arxiv.org/html/2609.28561#bib.bib35)\)\)\.

We use a batch size of 256 and set the loss coefficientλCARE\\lambda\_\{\\text\{CARE\}\}to 0\.25 by default\. Unless otherwise specified, CARE is applied to the last layer of the SiT model and the condition\-agnostic weightα\\alphais set as0\.50\.5\.

Text\-to\-Image GenerationOur experiments on text\-to\-image generation are conducted on a 24\-layer MMDiT model, consistent with the same setup in\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)\. We perform experiments on one of the pretrain datasets of LLaVA\([Liu et al\., 2023a](https://arxiv.org/html/2609.28561#bib.bib24)\), which is a subset of the CC3M dataset\([Sharma et al\., 2018](https://arxiv.org/html/2609.28561#bib.bib25)\)containing 595k images at 256×\\times256 resolution and captions relabeled with GPT\. We train the MMDiT model following the training settings in\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)\.

The condition inputs of the MMDiT and CARE are generated by of CLIP\-L\([Radford et al\., 2021](https://arxiv.org/html/2609.28561#bib.bib26)\)text encoder\. We apply CARE to the 8th layer of the MMDiT model\. For evaluation, we sample 50,000 images from prompts the dataset and report the FID\([Heusel et al\., 2017](https://arxiv.org/html/2609.28561#bib.bib7)\)and textual CLIP score\([Hessel et al\., 2021](https://arxiv.org/html/2609.28561#bib.bib27)\)\.

Combination with REPAFor experiments with the combination of REPA\([Yu et al\., 2025](https://arxiv.org/html/2609.28561#bib.bib2)\)in both tasks, we apply our method to the same layer as REPA, and use DINOv2\-B\([Oquab et al\., 2023](https://arxiv.org/html/2609.28561#bib.bib28)\)as the foundation model for alignment\. The final loss becomes

ℒ=ℒFM\+λREPA​ℒREPA\+λCARE​ℒCARE\.\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{FM\}\}\+\\lambda\_\{\\text\{REPA\}\}\\mathcal\{L\}\_\{\\text\{REPA\}\}\+\\lambda\_\{\\text\{CARE\}\}\\mathcal\{L\}\_\{\\text\{CARE\}\}\.\(8\)The loss weightλREPA\\lambda\_\{\\text\{REPA\}\}is set to0\.50\.5in class\-to\-image task and 0\.25 in text\-to\-image task\. Unless otherwise specified, the loss coefficientλCARE\\lambda\_\{\\text\{CARE\}\}is fixed to 0\.25 across all tasks\.

Alignment with Text ConditionTo quantify how well intermediate representations align with text conditions, we adopt a linear probing protocol\. Specifically, we extract model representations by settingt=0t=0, corresponding to clean inputs, and feed the empty token as the conditional input to remove explicit conditioning signals during representation extraction\. The resulting representations are split into training and validation sets with a 9:1 ratio\.

We then train a single\-layer linear probe to predict text condition embeddings by minimizing the negative cosine similarity\. The probe is trained with a batch size of 16384 and a learning rate of 0\.001\. Following common practice, we report the highest average cosine similarity on the validation set as the alignment score of the diffusion model\.

### 4\.2Main Results

We summarize our empirical findings across class\-conditional generation and text\-to\-image \(T2I\) tasks\. Our proposedCARE\(Condition\-Aware REpresentation regularization\) \(1\) consistently significantly improves generation quality across various benchmarks, \(2\) serves as an effective, complementary regularizer to existing objectives, and \(3\) promotes a stronger conditional semantic structure within the intermediate representation space\.

##### CARE improves generation performance across tasks and models\.

We first evaluate CARE as a standalone regularization objective, denoted asCARE\. Comparisons are made against vanilla SiT and MMDiT models, as well as versions regularized by the dispersive loss, a condition\-agnostic and parameter\-free baseline\. Quantitative results are reported in Table[1](https://arxiv.org/html/2609.28561#S4.T1)\.

ImageNet\.As shown in[Figure2](https://arxiv.org/html/2609.28561#S0.F2), CARE yields consistent performance improvements throughout training\. For SiT\-B/2 at 400k steps, CARE reduces the FID from 33\.02 to29\.71\. Larger gains are observed on SiT\-XL/2: at 400k steps, the FID decreases from 17\.19 to13\.91, a relative improvement of 19\.08%\. When CFG is applied, the improvement becomes substantially larger: the FID further decreases from 5\.36 to4\.09, corresponding to a 23\.69% relative gain\. Notably, CARE also significantly improves training efficiency: our SiT\-XL/2 model with CARE trained for 2\.4M steps achieves lower FID than the baseline SiT\-XL/2 trained for 7M steps, which corresponds to the reported convergence regime in prior work\.

![Refer to caption](https://arxiv.org/html/2609.28561v1/imagenet_visual.png)Figure 4:Qualitative comparison on ImageNet 256×\\times256\. Both models share the same noise, and use a Euler ODE sampler, 50 steps, and CFG scale4\.04\.0for sampling\.Text\-to\-image tasks\.CARE also improves both generation quality and alignment with textual conditions\. At 200k steps, CARE reduces FID from 11\.32 to9\.44, a 16\.61% relative improvement\. By 300k steps, the FID further decreases from 8\.77 to7\.02, a 19\.95% improvement\. In addition, CARE consistently raises the textual CLIP score throughout training\.

##### CARE produces complementary improvements\.

We combine CARE with REPA to assess whether CARE provides orthogonal benefits to existing representation–regularization approaches\. Across both class\-to\-image and text\-to\-image settings, the two methods show strongly complementary and synergistic effects\.

As shown in[Table1](https://arxiv.org/html/2609.28561#S4.T1), adding CARE on top of REPA leads to further gains across models in class\-to\-image generation\. On SiT\-B/2, REPA alone reaches an FID of 24\.31, while the combination of REPA and CARE reduces it to21\.64, corresponding to a relative improvement of 10\.98%\. A similar trend is observed on SiT\-XL/2, where pairing CARE with REPA improves the FID from 8\.81 to8\.31, confirming that CARE provides an additional, orthogonal source of regularization\.

##### CARE promotes better conditional structure of representations\.

To better understand the underlying mechanism, we quantify how well intermediate representations align with conditioning signals in the text\-to\-image setting, following the evaluation protocol in[Section4\.1](https://arxiv.org/html/2609.28561#S4.SS1)\. As shown in[Figure3](https://arxiv.org/html/2609.28561#S1.F3), CARE consistently improves condition–representation alignment throughout training, with additional gains when combined with REPA\. These results indicate that CARE effectively strengthens the conditional structure of the representation space and provides a clearer semantic organization of learned features\.

### 4\.3Ablation Studies

#### 4\.3\.1Effect of Condition\-Agnostic Weightα\\alpha

CARE introduces a key hyperparameter,α\\alpha, which controls the strength of the condition\-dependent supervision\. Whenα=1\.0\\alpha=1\.0, the regularizer becomes fully condition\-agnostic\. As shown in[Tables2](https://arxiv.org/html/2609.28561#S4.T2)and[3](https://arxiv.org/html/2609.28561#S4.T3), the influence ofα\\alphaexhibits a consistent pattern across both class\-to\-image without REPA and text\-to\-image experiments\. Moderate values such asα=0\.5\\alpha=0\.5generally yield the best trade\-off, while the purely condition\-agnostic variant tends to perform the worst\.

When CARE is combined with REPA on class\-conditioned ImageNet, the optimal choice ofα\\alphashifts toward smaller values\. In particular,α\\alphain the range of0\.010\.01to0\.0010\.001leads to the strongest improvements\. We posit that the presence of external supervision in REPA amplifies the benefit of smallerα\\alpha, as weaker condition\-agnosticity encourages the representation to more directly align with REPA’s optimization objective\.

Table 2:Effect ofα\\alphaon ImageNet with and without REPA\. Evaluated using an ODE sampler for 250 steps \(without CFG\)\.w/o REPAw/ REPA𝜶\\boldsymbol\{\\alpha\}FID↓\\downarrowIS↑\\uparrowFID↓\\downarrowIS↑\\uparrowbaseline34\.8441\.5324\.3162\.231\.032\.7944\.8023\.3664\.790\.530\.9147\.2223\.2864\.880\.2531\.5546\.1723\.1864\.310\.05––22\.2567\.330\.01––21\.6468\.500\.001––21\.8369\.35Table 3:Effect of theα\\alphaparameter on text\-to\-image generation, with and without REPA\. All results are evaluated using an ODE sampler \(50 steps\) with CFG scale=2\.0=2\.0\.w/o REPAw/ REPA𝜶\\boldsymbol\{\\alpha\}FID↓\\downarrowCLIP\-T↑\\uparrowFID↓\\downarrowCLIP\-T↑\\uparrowbaseline11\.3218\.258\.1619\.251\.09\.9818\.607\.8019\.600\.759\.7718\.628\.1219\.620\.59\.4418\.547\.4419\.660\.259\.6918\.537\.6719\.69
#### 4\.3\.2Effect of Similarity Measurement

We investigate two formulations of the similarity function described in[Section3\.4\.2](https://arxiv.org/html/2609.28561#S3.SS4.SSS2):linearandsoftmax\. These two variants represent*absolute*and*relative*similarity measurements, respectively\.

As shown in[Table4](https://arxiv.org/html/2609.28561#S4.T4), both formulations yield significant gains in sample quality \(FID\) and condition alignment \(CLIP\-T\) compared to the baseline\. The linear measure, which directly evaluates feature affinity, provides slightly better overall sample quality, while the softmax form, emphasizing relative contextual similarity, enhances condition alignment\. These results suggest that CARE’s effectiveness is robust across different similarity metrics\.

Table 4:Ablation results of similarity measure in text\-to\-image generation\. Evaluated using an ODE sampler for 50 stepswithCFG scale=2\.0=2\.0𝜶\\boldsymbol\{\\alpha\}𝒔⁡\(⋅\)\\boldsymbol\{s\(\\cdot\)\}FID↓\\downarrowCLIP\-T↑\\uparrowbaselinew/o CARE11\.3218\.250\.25linear9\.6918\.53softmax\(τc=1\)\(\\tau\_\{c\}=1\)9\.7618\.62softmax\(τc=0\.5\)\(\\tau\_\{c\}=0\.5\)9\.7718\.550\.5linear9\.4418\.54softmax\(τc=1\)\(\\tau\_\{c\}=1\)9\.8818\.57softmax\(τc=0\.5\)\(\\tau\_\{c\}=0\.5\)9\.5818\.64
#### 4\.3\.3Effect of Loss CoefficientλCARE\\lambda\_\{\\text\{CARE\}\}

We investigate the impact of the loss coefficientλCARE\\lambda\_\{\\text\{CARE\}\}on ImageNet256×256256\\times 256, both with and without REPA\. As shown in[Table5](https://arxiv.org/html/2609.28561#S4.T5), introducing CARE with a moderate coefficient consistently improves generation quality over the baseline\. Without REPA, settingλCARE=0\.25\\lambda\_\{\\text\{CARE\}\}=0\.25leads to a substantial improvement, reducing FID from 34\.84 to 30\.91 while increasing IS from 41\.53 to 47\.22\. Increasing the coefficient to0\.50\.5results in slightly degraded performance, indicating that excessively strong regularization may begin to interfere with the original diffusion training objective\.

When combined with REPA, bothλCARE=0\.25\\lambda\_\{\\text\{CARE\}\}=0\.25and0\.50\.5further improve upon the REPA baseline\. In particular,λCARE=0\.5\\lambda\_\{\\text\{CARE\}\}=0\.5achieves the best FID \(21\.57\), whileλCARE=0\.25\\lambda\_\{\\text\{CARE\}\}=0\.25yields the highest IS \(68\.50\)\. Overall, these results suggest that CARE is not overly sensitive to the precise choice ofλCARE\\lambda\_\{\\text\{CARE\}\}, and relatively small coefficients are sufficient to obtain significant gains\.

Table 5:Effect of the loss coefficientλCARE\\lambda\_\{\\text\{CARE\}\}on ImageNet 256×\\times256, with and without REPA\. All results are evaluated using an ODE samplers for 250 steps \(without CFG\)\.w/o REPAw/ REPA𝝀CARE\\boldsymbol\{\\lambda\}\_\{\\textbf\{CARE\}\}FID↓\\downarrowIS↑\\uparrowFID↓\\downarrowIS↑\\uparrowbaseline34\.8441\.5324\.3162\.230\.2530\.9147\.2221\.6468\.500\.532\.2745\.2521\.5768\.35
#### 4\.3\.4Effect of Injection Depth

We study the effect of injecting CARE at different intermediate layers of the diffusion model\. As shown in[Table6](https://arxiv.org/html/2609.28561#S4.T6), injecting CARE at deeper layers consistently leads to better generation quality, reflected by both lower FID and higher IS\.

Specifically, applying CARE at shallow layers yields only marginal improvements over the baseline\. Injecting CARE at layer 12, corresponding to the final transformer block in SiT\-B/2, achieves the best results\.

We attribute this trend to the fact that CARE acts directly on the representations used for conditional generation\. When injected at deeper layers, CARE more directly influences the representations that are propagated to the output, making its regularization effect more effective\. In contrast, regularization applied at earlier layers may be partially attenuated by subsequent transformations\.

Table 6:Effect of CARE injection layer on ImageNet 256×\\times256 using SiT\-B/2 \(a 12\-layer model\)\. All results are evaluated using an ODE sampler for 250 steps \(without CFG\)\.LayerFID↓\\downarrowIS↑\\uparrowbaseline34\.8441\.53434\.4642\.61832\.6944\.881230\.9147\.22
#### 4\.3\.5Enforcing Distinct Labels within Local Batch

To examine whether distancing intra\-class representations contributes to effective representation regularization, we conduct an ablation study where each local batch used for the regularization loss contains samples from distinct class labels on ImageNet256×256256\\times 256\. From a contrastive learning perspective, this ensures that no two samples in the batch share the same label, functioning as false negative cancellation\([Huynh et al\., 2022](https://arxiv.org/html/2609.28561#bib.bib32)\)\.

[Table7](https://arxiv.org/html/2609.28561#S4.T7)shows that this modification yields a moderate improvement for the standard dispersive loss, reducing FID from 32\.79 to 32\.07\.This indicates that avoiding false negatives indeed benefits representation learning\.However, the improvement remains smaller than that of CARE, which further achieves an FID of 30\.94\.

We attribute this to the design of CARE, which does not simply avoid false negatives but instead learns the relative structure of representations across conditions \- adding a relatively small penalty for clustering of representations with similar conditions\.

Table 7:Ablation results on enforcing label distinctness within local batch \(d\-sampler\)\. Evaluated using an ODE sampler for 250 stepswithoutCFGMethodIter\.FID↓\\downarrowIS↑\\uparrowSiT\-B/2 \+ disp\. loss400k32\.7944\.80SiT\-B/2 \+ disp\. loss \+ d\-sampler400k32\.0745\.50SiT\-B/2 \+ CARE400k30\.9447\.22

### 4\.4Generalizing to other supervision signals

The framework of CARE can be generalized to scenarios where other supervision signals are available\. For instance, we replaced the text conditions in CARE with the image class tokens of the DINOv2 model\. When conducting experiments on text\-image generation combined with REPA, this modification further improves the FID from7\.44to7\.27compare to CARE with text class token, suggesting that supervised signals derived from pretrained vision models can provide more semantically aligned guidance than textual conditions\.

## 5Discussions and Conclusion

Connection with dispersive loss\.Dispersive loss\([Wang and He, 2025](https://arxiv.org/html/2609.28561#bib.bib3)\)can be viewed as a special case of CARE, whereψ⁡\(⋅\)\\psi\(\\cdot\)is a constant mapping and thereby the conditional supervision is removed, obtaining an unsupervised contrastive loss that is condition\-agnostic\.

Limitations and future work\.Our study focuses in large part on categorical and textual conditions and is limited to diffusion models for image generation\. Exploring the applicability of CARE to richer supervision, such as multimodal conditioning, or extending CARE to video, audio, or 3D content generative frameworks are promising directions for future work\.

Conclusion\.We introduced CARE, a lightweight condition\-aware regularization method that uses built\-in conditioning signals to improve the semantic structure of diffusion representations\. CARE is theoretically connected to mutual\-information maximization and empirically enhances sample quality for both class\-to\-image and text\-to\-image tasks\. It requires no external models and complements existing approaches, offering a distinct and synergistic source of improvement\.

## Impact Statement

This paper presents work whose goal is to advance the field of Machine Learning\. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here\.

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## Appendix AHeuristic Interpretation of CARE via Mutual Information

In this appendix, we provide a heuristic interpretation of the CARE objective from the perspective of conditional mutual information under the class\-conditional setting\. We emphasize that this analysis is*not*required for defining or optimizing CARE; rather, it serves to offer intuition on how the proposed regularizer encourages structured conditional representations\.

##### From mutual information to conditional likelihood

Given a batch of representation–condition pairs\{\(𝐳i,𝐜i\)\}i=1N\\\{\(\\mathbf\{z\}\_\{i\},\\mathbf\{c\}\_\{i\}\)\\\}\_\{i=1\}^\{N\}\. From a probabilistic perspective, this behavior can be interpreted as encouraging dependence between the representation variableZθZ\_\{\\theta\}and the condition variableCC\. A natural quantity that captures such dependence is the mutual information

I⁡\(Zθ,C\)=H⁡\(C\)−H⁡\(C∣Zθ\),I\(Z\_\{\\theta\};C\)=H\(C\)\-H\(C\\mid Z\_\{\\theta\}\),\(9\)whereZθZ\_\{\\theta\}andCCfollow the joint distributionpθ​\(z,c\)p\_\{\\theta\}\(z,c\)induced by the data and the model\. SinceH⁡\(C\)H\(C\)is independent of model parameters, maximizingI⁡\(Zθ,C\)I\(Z\_\{\\theta\};C\)is equivalent to minimizing the conditional entropyH⁡\(C∣Zθ\)H\(C\\mid Z\_\{\\theta\}\), or equivalently maximizing

𝔼pθ​\(z,c\)​\[log⁡p⁡\(C∣Zθ\)\]\.\\mathbb\{E\}\_\{p\_\{\\theta\}\(z,c\)\}\\big\[\\log p\(C\\mid Z\_\{\\theta\}\)\\big\]\.\(10\)

##### Kernel\-based surrogate for the conditional likelihood\.

Directly optimizing the conditional likelihoodp⁡\(C∣Zθ\)p\(C\\mid Z\_\{\\theta\}\)is intractable, as this distribution is implicit and evolves with model parameters\. Instead, we seek a tractable surrogate objective that captures the same inductive bias: representations corresponding to similar conditions should exhibit stronger geometric coherence\.

To this end, we adopt a nonparametric kernel\-based approximation ofp⁡\(C∣Zθ\)p\(C\\mid Z\_\{\\theta\}\)using Nadaraya–Watson regression\([Nadaraya, 1964](https://arxiv.org/html/2609.28561#bib.bib33);[Watson, 1964](https://arxiv.org/html/2609.28561#bib.bib34)\)\. For clarity, we focus on discrete conditions\. LettingX=ZθX=Z\_\{\\theta\}andY=𝟙\{C=𝐜\}Y=\\mathds\{1\}\\\{C=\\mathbf\{c\}\\\}, the conditional probability can be estimated from a batch as

p^​\(𝐜∣𝐳\)=∑i=1Nϕ\(𝐳,𝐳i\)1\{𝐜i=𝐜\}∑i=1Nϕ⁡\(𝐳,𝐳i\),\\hat\{p\}\(\\mathbf\{c\}\\mid\\mathbf\{z\}\)=\\frac\{\\sum\_\{i=1\}^\{N\}\\phi\(\\mathbf\{z\},\\mathbf\{z\}\_\{i\}\)\\,\\mathds\{1\}\\\{\\mathbf\{c\}\_\{i\}=\\mathbf\{c\}\\\}\}\{\\sum\_\{i=1\}^\{N\}\\phi\(\\mathbf\{z\},\\mathbf\{z\}\_\{i\}\)\},\(11\)whereϕ⁡\(⋅,⋅\)\\phi\(\\cdot,\\cdot\)is a kernel defined in the representation space\.

To avoid numerical issues, we use a smoothed estimation

p~​\(𝐜∣𝐳\)=\(1−ϵ\)​p^​\(𝐜∣𝐳\)\+ϵ/K,\\displaystyle\\tilde\{p\}\(\\mathbf\{c\}\\mid\\mathbf\{z\}\)=\(1\-\\epsilon\)\\hat\{p\}\(\\mathbf\{c\}\\mid\\mathbf\{z\}\)\+\\epsilon/K,\(12\)whereϵ\>0\\epsilon\>0is a small constant andKKis the total number of classes\.

##### A tractable surrogate objective\.

Using the kernel\-based estimate ofp⁡\(C∣Zθ\)p\(C\\mid Z\_\{\\theta\}\), one can construct a negative log\-likelihood objective over a batch, which takes the form

ℒ=−∑i=1Nlogp~\(𝐜i∣𝐳i\),\\mathcal\{L\}=\-\\sum\_\{i=1\}^\{N\}\\log\\tilde\{p\}\(\\mathbf\{c\}\_\{i\}\\mid\\mathbf\{z\}\_\{i\}\),\(13\)
To obtain a compact and tractable form, we follow a common approximation used in contrastive learning\([Wang and Isola, 2020](https://arxiv.org/html/2609.28561#bib.bib4)\), which swaps the order of the summation and the logarithm\. Although this approximation is not exact, it leads to a decomposed objective consisting of a supervised, condition\-aware term and an unsupervised uniformity regularization term \(ℒuniformity\\mathcal\{L\}\_\{\\text\{uniformity\}\}, as in[Wang and Isola \(2020\)](https://arxiv.org/html/2609.28561#bib.bib4)\)\.

ℒnll=\\displaystyle\\mathcal\{L\}\_\{\\text\{nll\}\}=−log⁡\(∑1≤i,j≤NWi,j​ϕ​\(𝐳i,𝐳j\)\)\+log⁡\(∑1≤i,j≤Nϕ⁡\(𝐳i,𝐳j\)\)⏟ℒuniformity,\\displaystyle\{\-\\log\\left\(\{\\sum\_\{1\\leq i,j\\leq N\}W\_\{i,j\}\\phi\\left\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\\right\)\}\\right\)\}\+\\underbrace\{\\log\\left\(\\sum\_\{1\\leq i,j\\leq N\}\\phi\\left\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\\right\)\\right\)\}\_\{\\mathcal\{L\}\_\{\\text\{uniformity\}\}\},whereWi,j=\(1−ϵ\)𝟙\{ci=cj\}\+ϵ/KW\_\{i,j\}=\(1\-\\epsilon\)\\mathds\{1\}\\left\\\{c\_\{i\}=c\_\{j\}\\right\\\}\+\\epsilon/K\.

To explicitly control the balance between these two effects, we introduce a coefficientγ\\gammaand obtain the surrogate objective

ℒγ=ℒnll\+γ​ℒuniformity,\\mathcal\{L\}\_\{\\gamma\}=\\mathcal\{L\}\_\{\\text\{nll\}\}\+\\gamma\\,\\mathcal\{L\}\_\{\\text\{uniformity\}\},\(14\)

##### Simplified form under class\-conditional structure\.

For discrete conditions, let

X=∑𝐜i=𝐜jϕ⁡\(𝐳i,𝐳j\),Y=∑𝐜i≠𝐜jϕ⁡\(𝐳i,𝐳j\)\.X=\\sum\_\{\\mathbf\{c\}\_\{i\}=\\mathbf\{c\}\_\{j\}\}\\phi\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\),\\qquad Y=\\sum\_\{\\mathbf\{c\}\_\{i\}\\neq\\mathbf\{c\}\_\{j\}\}\\phi\(\\mathbf\{z\}\_\{i\},\\mathbf\{z\}\_\{j\}\)\.With a smoothing constantβ\\betainduced by label smoothing, the objectiveℒγ\\mathcal\{L\}\_\{\\gamma\}can be rewritten \(up to an additive constant\) as

ℒβ,γ=−log⁡\(X\+β​Y\)\+\(1\+γ\)​log⁡\(X\+Y\)\.\\mathcal\{L\}\_\{\\beta,\\gamma\}=\-\\log\\left\(X\+\\beta Y\\right\)\+\(1\+\\gamma\)\\log\\left\(X\+Y\\right\)\.\(15\)

##### Resulting CARE form\.

Under the empirical observation that the ratior=Y/Xr=Y/Xquickly becomes small during training \(see[Figure5](https://arxiv.org/html/2609.28561#A1.F5)\),ℒβ,γ\\mathcal\{L\}\_\{\\beta,\\gamma\}admits a first\-order approximation that leads to a concise form

ℒ=log⁡\(α​X\+Y\),0<α<1,\\mathcal\{L\}=\\log\\left\(\\alpha X\+Y\\right\),\\qquad 0<\\alpha<1,\(16\)whereα\\alphaabsorbs the effects ofγ\\gammaandβ\\betaas follows

ℒβ,γ\\displaystyle\\mathcal\{L\}\_\{\\beta,\\gamma\}=γ​log⁡X\+\(1\+γ−β\)​r\+𝒪⁡\(r2\)\\displaystyle=\\gamma\\log X\+\\left\(1\+\\gamma\-\\beta\\right\)r\+\\mathcal\{O\}\(r^\{2\}\)\(17\)=γ​log⁡\(γ1\+γ−β​X\+Y\)\+C\+𝒪⁡\(r2\)\.\\displaystyle=\\gamma\\log\\left\(\\frac\{\\gamma\}\{1\+\\gamma\-\\beta\}X\+Y\\right\)\+C\+\\mathcal\{O\}\(r^\{2\}\)\.\(18\)
[Equation16](https://arxiv.org/html/2609.28561#A1.E16)is exactly the formalization of CARE under class\-conditioned settings \(see[Section3\.4\.1](https://arxiv.org/html/2609.28561#S3.SS4.SSS1)\)\.

Figure 5:Evolution of the ratior=Y/Xr=Y/Xover training steps of CARE\. The ratio quickly decreases to the order of10−410^\{\-4\}after several hundreds steps\.

## Appendix BAdditional Visual Results on ImageNet 256×\\times256

![Refer to caption](https://arxiv.org/html/2609.28561v1/assets/2.4m-care.jpeg)Figure 6:Uncurated samples generated by SiT\-XL/2 trained with CARE for 2\.4M iterations\. Best view zoom in\. Sampling uses a 50\-step ODE sampler with CFG scale 4\.0\.