Modeling and sampling from the underlying distribution of asynchronous event sequences are crucial in various real-world applications, including social networks, medical diagnosis, and financial transactions. Existing autoregressive methods suffer from error accumulation during multi-step generation, while non-autoregressive diffusion methods are typically limited to fixed-length output sequences. In this paper, we propose Latent Block-Diffusion Temporal Point Processes (LBDTPP), a novel semi-autoregressive TPP framework that introduces a latent block diffusion mechanism for high-quality and variable-length event sequence generation. The core idea is to define an autoregressive probability distribution over event blocks in latent space and perform Gaussian diffusion within each block. By sequentially generating blocks while simultaneously sampling events in each block, LBDTPP preserves the length flexibility of autoregressive TPPs and inherits the parallel high-quality generation capability of diffusion models. Theoretically, we derive Wasserstein error bounds showing that, under suitable local approximation and prefix-stability assumptions, block-wise generation can reduce error accumulation compared with event-wise autoregressive generation. Extensive experiments on six real-world benchmark datasets demonstrate that LBDTPP outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks. Further empirical analyses verify the benefits of latent-space diffusion and block-wise generation, and reveal the trade-off between generation quality and block size. Our code is available at https://github.com/Zh-Shuai/LBDTPP.

We argue that diffusion models' success in modeling complex distributions is, for the most part, coming from their input conditioning. This paper investigates the representation used to condition diffusion models from the perspective that ideal representations should improve sample fidelity, be easy to generate, and be compositional to allow out-of-training samples generation. We introduce Discrete Latent Code (DLC), an image representation derived from Simplicial Embeddings trained with a self-supervised learning objective. DLCs are sequences of discrete tokens, as opposed to the standard continuous image embeddings. They are easy to generate and their compositionality enables sampling of novel images beyond the training distribution. Diffusion models trained with DLCs have improved generation fidelity, establishing a new state-of-the-art for unconditional image generation on ImageNet. Additionally, we show that composing DLCs allows the image generator to produce out-of-distribution samples that coherently combine the semantics of images in diverse ways. Finally, we showcase how DLCs can enable text-to-image generation by leveraging large-scale pretrained language models. We efficiently finetune a text diffusion language model to generate DLCs that produce novel samples outside of the image generator training distribution.

Classifier-free guidance (CFG) has become an essential component of modern diffusion models to enhance both generation quality and alignment with input conditions. However, CFG requires specific training procedures and is limited to conditional generation. To address these limitations, we propose Token Perturbation Guidance (TPG), a novel method that applies perturbation matrices directly to intermediate token representations within the diffusion network. TPG employs a norm-preserving shuffling operation to provide effective and stable guidance signals that improve generation quality without architectural changes. As a result, TPG is training-free and agnostic to input conditions, making it readily applicable to both conditional and unconditional generation. We further analyze the guidance term provided by TPG and show that its effect on sampling more closely resembles CFG compared to existing training-free guidance techniques. Extensive experiments on SDXL and Stable Diffusion 2.1 show that TPG achieves nearly a 2 improvement in FID for unconditional generation over the SDXL baseline, while closely matching CFG in prompt alignment. These results establish TPG as a general, condition-agnostic guidance method that brings CFG-like benefits to a broader class of diffusion models.

Classifier-free guidance (CFG) has become an essential component of modern diffusion models to enhance both generation quality and alignment with input conditions. However, CFG requires specific training procedures and is limited to conditional generation. To address these limitations, we propose Token Perturbation Guidance (TPG), a novel method that applies perturbation matrices directly to intermediate token representations within the diffusion network. TPG employs a norm-preserving shuffling operation to provide effective and stable guidance signals that improve generation quality without architectural changes. As a result, TPG is training-free and agnostic to input conditions, making it readily applicable to both conditional and unconditional generation. We also analyze the guidance term provided by TPG and show that its effect on sampling more closely resembles CFG compared to existing training-free guidance techniques. We extensively evaluate TPG on SDXL and Stable Diffusion 2.1, demonstrating nearly a 2x improvement in FID for unconditional generation over the SDXL baseline and showing that TPG closely matches CFG in prompt alignment. Thus, TPG represents a general, condition-agnostic guidance method that extends CFG-like benefits to a broader class of diffusion models.

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mapping between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM achieves better sample quality than representative baselines while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.

Unconditional generation--the problem of modeling data distribution without relying on human-annotated labels--is a long-standing and fundamental challenge in generative models, creating a potential of learning from large-scale unlabeled data. In the literature, the generation quality of an unconditional method has been much worse than that of its conditional counterpart. This gap can be attributed to the lack of semantic information provided by labels. In this work, we show that one can close this gap by generating semantic representations in the representation space produced by a self-supervised encoder. These representations can be used to condition the image generator.

Lately, there has been a surge in interest surrounding generative modeling of time series data. Most existing approaches are designed either to process short sequences or to handle long-range sequences. This dichotomy can be attributed to gradient issues with recurrent networks, computational costs associated with transformers, and limited expressiveness of state space models. Towards a unified generative model for varying-length time series, we propose in this work to transform sequences into images.

Understanding brain function represents a fundamental goal in neuroscience, with critical implications for therapeutic interventions and neural engineering applications. Computational modeling provides a quantitative framework for accelerating this understanding, but faces a fundamental trade-off between computational efficiency and high-fidelity modeling. To address this limitation, we introduce a novel Energy-based Autoregressive Generation (EAG) framework that employs an energy-based transformer learning temporal dynamics in latent space through strictly proper scoring rules, enabling efficient generation with realistic population and single-neuron spiking statistics. Evaluation on synthetic Lorenz datasets and two Neural Latents Benchmark datasets (MC Maze and Area2 bump) demonstrates that EAG achieves state-of-the-art generation quality with substantial computational efficiency improvements, particularly over diffusion-based methods. Beyond optimal performance, conditional generation applications show two capabilities: generalizing to unseen behavioral contexts and improving motor brain-computer interface decoding accuracy using synthetic neural data. These results demonstrate the effectiveness of energy-based modeling for neural population dynamics with applications in neuroscience research and neural engineering.