Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets. This mismatch can limit reconstruction accuracy, reduce sample quality, and constrain the expressive power of the learned latent space. We propose the eXact-Prior Variational Autoencoder (X-VAE), a framework that replaces the conventional standard normal prior with a Gaussian prior derived from the latent representations of a pretrained autoencoder (AE). Specifically, the empirical mean and standard deviation of the AE latent codes are used to parameterize a data-adaptive prior that more closely reflects the underlying structure of the training data. During generation, X-VAE introduces a latent scaling factor that enables explicit control over the variance of the sampled latent vectors, providing a simple mechanism for balancing sample diversity and fidelity. This flexibility makes the proposed approach particularly well suited for applications such as industrial and engineering design, where generated solutions must satisfy strict structural or functional constraints while still permitting meaningful design exploration. We present the mathematical formulation of well-suited X-VAE, derive the corresponding KL divergence objective for the proposed prior, and evaluate the method on standard benchmark datasets. Experimental results demonstrate that X-VAE preserves reconstruction quality while producing latent representations that better align with the empirical data distribution, leading to improved controllability and more realistic generated samples.

Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov $n$-widths. In the realm of Reduced-Order Modelling (ROM), these models are increasingly utilized to learn low-dimensional representations of solution manifolds associated with parametric Partial Differential Equations (PDEs). However, the high expressivity of AEs presents a challenge: although trained networks typically minimize reconstruction error, they often struggle to capture the essential properties necessary for building accurate and robust ROMs. Recent works by arXiv:2307.15288v2 and arXiv:2506.11641v1 have tackled this challenge in fully connected AEs by proposing representation-consistent architectures, which preserve some of the properties belonging to POD. This study builds upon that concept by extending representation consistency for convolutional layers. We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings. When integrated into a ROM framework, this architecture demonstrates significantly improved predictive capabilities. Specifically, we compared the performance of the ROMs based on classical and symmetric CAEs on three one dimensional academic test cases, namely the Linear Advection, the Viscous Burger and the Kuramoto Sivashinsky equation. Numerical results demonstrate that our proposed symmetric approach consistently yields more accurate latent trajectories, lower reconstruction errors, and enhanced model robustness.

Vector-Quantized Variational Autoencoders (VQVAEs) have enabled strong performance in generative modeling by mapping continuous data to learnable codes. In this work, we identify a surprising yet consistent phenomenon that we term dimensional collapse: despite using high-dimensional embeddings, VQVAEs tend to compress their representations into a much smaller subspace, typically only 4 to 10 dimensions. We provide an in-depth analysis of this phenomenon and reveal its relation to model performance and learning dynamics. Interestingly, VQVAEs naturally gravitate toward this low-dimensional regime, and enforcing higher-dimensional usage (e.g., via rank regularization) could lead to degraded performance. To overcome this low-dimensionality limitation, we propose Divide-and-Conquer VQ (DCVQ), which partitions the latent space into multiple low-dimensional subspaces, each quantized independently. By design, each subspace respects the model's preference for low dimensionality, while their combination expands the overall capacity. Our results show that DCVQ overcomes the inherent dimensional bottleneck and achieves improved reconstruction quality across image datasets.

Reward modeling, crucial for aligning large language models (LLMs) with human preferences, is often bottlenecked by the high cost of preference data. Existing textual data synthesis methods are computationally expensive. We propose a novel framework LENS for synthesizing preference data directly in the LLM's latent embedding space. Our method employs a Variational Autoencoder (VAE) to learn a structured latent representation of response embeddings. By performing controlled perturbations in this latent space and decoding back to the embedding space, we efficiently generate diverse, semantically consistent synthetic preference pairs, bypassing costly text generation and annotation. We provide theoretical guarantees that our synthesized pairs approximately preserve original preference ordering and improve reward model generalization. Empirically, our latent-space synthesis significantly outperforms text-based augmentation on standard benchmarks, achieving superior results while being 18 faster in generation and using a 16,000 smaller model. Our work offers a scalable and effective alternative for enhancing reward modeling through efficient data augmentation.

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

Diffusion models have achieved significant progress in image generation and the pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or pre-deblurred one as a conditional control for SD will either hinder accurate structure extraction or make the results overly dependent on the deblurring network. In this work, we propose a Latent Kernel Prediction Network (LKPN) to achieve robust realworld image deblurring.

In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose STSSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios.

LLMs have shown impressive capabilities across various natural language processing tasks, yet remain vulnerable to input prompts, known as jailbreak attacks, carefully designed to bypass safety guardrails and elicit harmful responses. Traditional methods rely on manual heuristics but suffer from limited generalizability. Despite being automatic, optimization-based attacks often produce unnatural prompts that can be easily detected by safety filters or require high computational costs due to discrete token optimization. In this paper, we introduce Generative Adversarial Suffix Prompter (GASP), a novel automated framework that can efficiently generate human-readable jailbreak prompts in a fully black-box setting. In particular, GASP leverages latent Bayesian optimization to craft adversarial suffixes by efficiently exploring continuous latent embedding spaces, gradually optimizing the suffix prompter to improve attack efficacy while balancing prompt coherence via a targeted iterative refinement procedure. Through comprehensive experiments, we show that GASP can produce natural adversarial prompts, significantly improving jailbreak success over baselines, reducing training times, and accelerating inference speed, thus making it an efficient and scalable solution for red-teaming LLMs. Warning: This paper contains text and examples that may be considered offensive or harmful.

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature's label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to "drift" noisy samples back to label-consistent representations. During adaptation, we sample from each target feature's latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier's accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve.