We introduce and study the Combinatorial Ski Rental (CSR) problem, which involves multiple items that can be rented or purchased, either individually or in combination. At each time step, a decision-maker must make an irrevocable buy-or-rent decision for items that have not yet been purchased, without knowing the end of the time horizon. We propose a randomized online algorithm, Sorted Optimal Amortized Cost (SOAC), that achieves the optimal competitive ratio. Moreover, SOAC can be extended to address various well-known ski rental variants, including the multi-slope, multi-shop, multi-commodity ski rental and CSR with upgrading problems. Building on the proposed SOAC algorithm, we further develop a learning-augmented algorithm that leverages machine-learned predictions to improve the performance of CSR. This algorithm is capable of recovering or improving upon existing results of learning-augmented algorithms in both the classic ski rental and multi-shop ski rental problems. Experimental results validate our theoretical analysis and demonstrate the advantages of our algorithms over baseline methods for ski rental problems.

Controlling the spatial and semantic structure of diffusion-generated images remains a challenge. Existing methods like ControlNet rely on handcrafted condition maps and retraining, limiting flexibility and generalization. Inversion-based approaches offer stronger alignment but incur high inference cost due to dual-path denoising. We present \textbf{FreeControl}, a training-free framework for semantic structural control in diffusion models. Unlike prior methods that extract attention across multiple timesteps, FreeControl performs \textit{one-step attention extraction} from a single, optimally chosen timestep and reuses it throughout denoising. This enables efficient structural guidance without inversion or retraining. To further improve quality and stability, we introduce \textit{Latent-Condition Decoupling (LCD)}: a principled separation of the timestep condition and the noised latent used in attention extraction. LCD provides finer control over attention quality and eliminates structural artifacts. FreeControl also supports compositional control via reference images assembled from multiple sources, enabling intuitive scene layout design and stronger prompt alignment. FreeControl introduces a new paradigm for test-time control—enabling structurally and semantically aligned, visually coherent generation directly from raw images, with the flexibility for intuitive compositional design and compatibility with modern diffusion models at ~5\% additional cost.

Deep generative models have gained much attention given their ability to generate data for applications as varied as healthcare to financial technology to surveillance, and many more - the most popular models being generative adversarial networks (GANs) and variational auto-encoders (VAEs). Yet, as with all machine learning models, ever is the concern over security breaches and privacy leaks and deep generative models are no exception. In fact, these models have advanced so rapidly in recent years that work on their security is still in its infancy. In an attempt to audit the current and future threats against these models, and to provide a roadmap for defense preparations in the short term, we prepared this comprehensive and specialized survey on the security and privacy preservation of GANs and VAEs. Our focus is on the inner connection between attacks and model architectures and, more specifically, on five components of deep generative models: the training data, the latent code, the generators/decoders of GANs/VAEs, the discriminators/encoders of GANs/VAEs, and the generated data. For each model, component and attack, we review the current research progress and identify the key challenges. The paper concludes with a discussion of possible future attacks and research directions in the field.