Old-photo face restoration poses significant challenges due to compounded degradations such as breakage, fading, and severe blur. Existing pre-trained diffusionguided methods either rely on explicit degradation priors or global statistical guidance, which struggle with localized artifacts or face color. We propose SelfSupervised Selective-Guided Diffusion (SSDiff), which leverages pseudo-reference faces generated by a pre-trained diffusion model under weak guidance. These pseudo-labels exhibit structurally aligned contours and natural colors, enabling region-specific restoration via staged supervision: structural guidance applied throughout the denoising process and color refinement in later steps, aligned with the coarse-to-fine nature of diffusion.

Recent guidance methods in diffusion models steer reverse sampling by perturbing the model to construct an implicit weak model and guide generation away from it. Among these approaches, attention perturbation has demonstrated strong empirical performance in unconditional scenarios where classifier-free guidance is not applicable. However, existing attention perturbation methods lack principled approaches for determining where perturbations should be applied, particularly in Diffusion Transformer (DiT) architectures where quality-relevant computations are distributed across layers. In this paper, we investigate the granularity of attention perturbations, ranging from the layer level down to individual attention heads, and discover that specific heads govern distinct visual concepts such as structure, style, and texture quality. Building on this insight, we propose "HeadHunter", a systematic framework for iteratively selecting attention heads that align with user-centric objectives, enabling fine-grained control over generation quality and visual attributes. In addition, we introduce SoftPAG, which linearly interpolates each selected head's attention map toward an identity matrix, providing a continuous knob to tune perturbation strength and suppress artifacts. Our approach not only mitigates the oversmoothing issues of existing layer-level perturbation but also enables targeted manipulation of specific visual styles through compositional head selection.

Recent advances in Structure-based Drug Design (SBDD) have leveraged generative models for 3D molecular generation, predominantly evaluating model performance by binding affinity to target proteins. However, practical drug discovery necessitates high binding affinity along with synthetic feasibility and selectivity, critical properties that were largely neglected in previous evaluations. To address this gap, we identify fundamental limitations of conventional diffusion-based generative models in effectively guiding molecule generation toward these diverse pharmacological properties. We propose CBYG, a novel framework extending Bayesian Flow Network into a gradient-based conditional generative model that robustly integrates property-specific guidance. Additionally, we introduce a comprehensive evaluation scheme incorporating practical benchmarks for binding affinity, synthetic feasibility, and selectivity, overcoming the limitations of conventional evaluation methods. Extensive experiments demonstrate that our proposed CBYG framework significantly outperforms baseline models across multiple essential evaluation criteria, highlighting its effectiveness and practicality for real-world drug discovery applications.

Classifier-Free Guidance (CFG) is an essential component of text-to-image diffusion models, and understanding and advancing its operational mechanisms remains a central focus of research. Existing approaches stem from divergent theoretical interpretations, thereby limiting the design space and obscuring key design choices. To address this, we propose a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation. We demonstrate that CFG and its variants constitute a special case of single-step short-interval iteration, which is theoretically proven to exhibit inefficiency. To this end, we introduce Foresight Guidance (FSG), which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations.

Molecular docking is a fundamental technique in structure-based drug discovery, playing a critical role in predicting the binding poses of protein-ligand complexes. While traditional docking methods are generally reliable, they are often computationally expensive. Recent deep learning (DL) approaches have substantially accelerated docking and improved prediction accuracy; however, they frequently generate conformations that lack physical plausibility due to insufficient integration of physical priors. To deal with these challenges, we propose ForceFM, a novel force-guided model that integrates a force-guided network into the generation process, steering ligand poses toward low-energy, physically realistic conformations. Force guidance also halves inference cost compared with the unguided approaches. Importantly, replacing the guiding potential with diverse energy functions-including Vina, Glide, Gnina, and Confscore-preserves or improves performance, underscoring the method's generality and robustness. These results highlight ForceFM's ability to set new standards in docking accuracy and physical consistency, surpassing the limitations of previous methods.

We present STARFlow, a scalable generative model based on normalizing flows that achieves strong performance on high-resolution image synthesis. STARFlow's main building block is Transformer Autoregressive Flow (TARFlow), which combines normalizing flows with Autoregressive Transformer architectures and has recently achieved impressive results in image modeling. In this work, we first establish the theoretical universality of TARFlow for modeling continuous distributions. Building on this foundation, we introduce a set of architectural and algorithmic innovations that significantly enhance the scalability: (1) a deep-shallow design where a deep Transformer block captures most of the model's capacity, followed by a few shallow Transformer blocks that are computationally cheap yet contribute non-negligibly, (2) learning in the latent space of pretrained autoencoders, which proves far more effective than modeling pixels directly, and (3) a novel guidance algorithm that substantially improves sample quality. Crucially, our model remains a single, end-to-end normalizing flow, allowing exact maximum likelihood training in continuous space without discretization. STARFlow achieves competitive results in both class-and text-conditional image generation, with sample quality approaching that of state-of-the-art diffusion models. To our knowledge, this is the first successful demonstration of normalizing flows at this scale and resolution.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance by projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at the posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical understanding of these two techniques relative to the continuous ideal gradients. Motivated by this analysis, we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients.

We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic normal distribution, samples undergo sharp, discrete transitions, eventually forming distinct events of a desired distribution while progressively revealing finer structure. As this process is reversible, these transitions also occur in reverse, where intermediate states progressively merge, tracing a path back to the initial distribution. We demonstrate that these transitions can be detected as discontinuities in nth-order cross-fluctuations. For variance-preserving SDEs, we derive a closed-form for these cross-fluctuations that is efficiently computable for the reverse trajectory. We find that detecting these transitions directly boosts sampling efficiency, accelerates class-conditional and rare-class generation, and improves two zero-shot tasks-image classification and style transfer-without expensive grid search or retraining. We also show that this viewpoint unifies classical coupling and mixing from finite Markov chains with continuous dynamics while extending to stochastic SDEs and non Markovian samplers.

We demonstrate that architectures which traditionally are considered to be ill-suited for a task can be trained using inductive biases from another architecture. We call a network untrainable when it overfits, underfits, or converges to poor results even when tuning their hyperparameters. For example, fully connected networks overfit on object recognition while deep convolutional networks without residual connections underfit. The traditional answer is to change the architecture to impose some inductive bias, although the nature of that bias is unknown. We introduce guidance, where a guide network steers a target network using a neural distance function.

Diffusion models excel at capturing the natural design spaces of images, molecules, and biological sequences. However, for many applications, rather than merely generating designs that are natural, we aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require "differentiable" proxy models (e.g., classifier guidance) or computationally-expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). Here, we propose a new method, Soft Value-based Decoding in Diffusion models (SVDD), to address these challenges. SVDD is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, SVDD avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly use non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of SVDD across several domains, including image generation, molecule generation (optimization of docking scores, QED, SA), and DNA/RNA generation (optimization of activity levels). The code is available at https://github.com/masa-ue/SVDD.