We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in generative AI, reinforcement learning, and computational biology. We consider the common learning scenario where the dataset consists of majorly unlabeled data and a small set of data with noisy reward labels. Our approach leverages a learned reward function on the smaller data set as a pseudolabeler to label the unlabelled data. After pseudo-labelling, a conditional diffusion model (CDM) is trained on the data and samples are generated by setting a target value $a$ as the condition in CDM. From a theoretical standpoint, we show that this directed generator can effectively learn and sample from the reward-conditioned data distribution: 1. our model is capable of recovering the data's latent subspace representation.

Text-to-image diffusion models achieve high-fidelity image generation from natural language prompts. ControlNets extend these models by enabling conditioning on structural inputs (e.g., edge maps, depth, pose), providing fine-grained control over outputs. Yet their reliance on large, publicly scraped datasets and community fine-tuning makes them vulnerable to data poisoning. We introduce a model-poisoning attack that embeds a covert backdoor into a ControlNet, causing it to produce attacker-specified content when exposed to visual triggers, without textual prompts. Experiments show that poisoning only 1% of the fine-tuning corpus yields a 90-98% attack success rate, while 5% further strengthens the backdoor, all while preserving normal generation quality. To mitigate this risk, we propose clean fine-tuning (CFT): freezing the diffusion backbone and fine-tuning only the ControlNet on a sanitized dataset with a reduced learning rate. CFT lowers attack success rates on held-out data. These results expose a critical security weakness in open-source, ControlNet-guided diffusion pipelines and demonstrate that CFT offers a practical defense for responsible synthetic-data pipelines.

In this paper, we study the Schrödinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin-endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schrödinger potentials in a nonparametric way. In particular, we use kernel based Monte Carlo regression in the context of Picard iteration of a corresponding fixed point problem as considered in [5]. By preserving in the iteration positivity and contractivity in a Hilbert metric sense, we develop a provably convergent algorithm. Furthermore, we provide convergence rates for the potential estimates and prove their optimality. Finally, as an application, we propose a non-nested Monte Carlo procedure for the final dimensional distributions of the Schrödinger Bridge process, based on the constructed potentials and the forward-reverse simulation method for conditional diffusions developed in [2].

Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data.

Unsupervised anomaly segmentation aims to detect patterns that are distinct from any patterns processed during training, commonly called abnormal or out-of-distribution patterns, without providing any associated manual segmentations. Since anomalies during deployment can lead to model failure, detecting the anomaly can enhance the reliability of models, which is valuable in high-risk domains like medical imaging. This paper introduces Masked Modality Cycles with Conditional Diffusion (MMCCD), a method that enables segmentation of anomalies across diverse patterns in multimodal MRI. The method is based on two fundamental ideas. First, we propose the use of cyclic modality translation as a mechanism for enabling abnormality detection. Image-translation models learn tissue-specific modality mappings, which are characteristic of tissue physiology. Thus, these learned mappings fail to translate tissues or image patterns that have never been encountered during training, and the error enables their segmentation. Furthermore, we combine image translation with a masked conditional diffusion model, which attempts to `imagine' what tissue exists under a masked area, further exposing unknown patterns as the generative model fails to recreate them. We evaluate our method on a proxy task by training on healthy-looking slices of BraTS2021 multi-modality MRIs and testing on slices with tumors. We show that our method compares favorably to previous unsupervised approaches based on image reconstruction and denoising with autoencoders and diffusion models.

How much explicit guidance is necessary for conditional diffusion? We consider the problem of conditional sampling using an unconditional diffusion model and limited explicit guidance (e.g., a noised classifier, or a conditional diffusion model) that is restricted to a small number of time steps. We explore a model predictive control (MPC)-like approach to approximate guidance by simulating unconditional diffusion forward, and backpropagating explicit guidance feedback. MPC-approximated guides have high cosine similarity to real guides, even over large simulation distances. Adding MPC steps improves generative quality when explicit guidance is limited to five time steps.