Bokai Yan

Min Zhao, Hongzhou Zhu, Bokai Yan et al.

Recent video diffusion foundation models have achieved remarkable progress in high-quality video generation, yet turning them into real-time interactive video world models remains challenging. Interactive world models require controllable, causal, and low-latency rollout, which in practice demands a full pipeline spanning data construction, controllable fine-tuning, autoregressive training, few-step distillation, and streaming inference. In this work, we present minWM, a full-stack open-source framework for building real-time interactive video world models. minWM provides an end-to-end pipeline that converts existing bidirectional T2V/TI2V video foundation models into camera-controllable few-step autoregressive world models. Specifically, minWM first fine-tunes a bidirectional video diffusion model with camera control, and then applies the Causal Forcing / Causal Forcing++ pipeline, including AR diffusion training, causal ODE or causal consistency distillation, and asymmetric DMD, to distill it into a few-step autoregressive generator for low-latency rollout. The framework is modular and architecture-extensible: we instantiate it on representative open backbones, including Wan2.1-T2V-1.3B and HY1.5-TI2V-8B, covering both cross-attention-based condition injection and MMDiT-style architectures. minWM also supports adapting existing video world models, such as HY-WorldPlay, to new data distributions, training recipes, and latency targets. Beyond releasing runnable scripts, checkpoints, documentation, and inference code, we provide practical ablations on camera trajectory quality, controllability training steps, and minimal batch-size requirements. We hope minWM serves as a reproducible and extensible recipe for building and adapting real-time interactive video world models. Project Page: [https://github.com/shengshu-ai/minWM](https://github.com/shengshu-ai/minWM)

Jose A. Carrillo, Bokai Yan

In this work we numerically study the diffusive limit of run & tumble kinetic models for cell motion due to chemotaxis by means of asymptotic preserving schemes. It is well-known that the diffusive limit of these models leads to the classical Patlak-Keller-Segel macroscopic model for chemotaxis. We will show that the proposed scheme is able to accurately approximate the solutions before blow-up time for small parameter. Moreover, the numerical results indicate that the global solutions of the kinetic models stabilize for long times to steady states for all the analyzed parameter range. We also generalize these asymptotic preserving schemes to two dimensional kinetic models in the radial case. The blow-up of solutions is numerically investigated in all these cases.

Min Zhao, Hongzhou Zhu, Kaiwen Zheng et al.

Real-time interactive video generation requires low-latency, streaming, and controllable rollout. Existing autoregressive (AR) diffusion distillation methods have achieved strong results in the chunk-wise 4-step regime by distilling bidirectional base models into few-step AR students, but they remain limited by coarse response granularity and non-negligible sampling latency. In this paper, we study a more aggressive setting: frame-wise autoregression with only 1--2 sampling steps. In this regime, we identify the initialization of a few-step AR student as the key bottleneck: existing strategies are either target-misaligned, incapable of few-step generation, or too costly to scale. We propose \textbf{Causal Forcing++}, a principled and scalable pipeline that uses \emph{causal consistency distillation} (causal CD) for few-step AR initialization. The core idea is that causal CD learns the same AR-conditional flow map as causal ODE distillation, but obtains supervision from a single online teacher ODE step between adjacent timesteps, avoiding the need to precompute and store full PF-ODE trajectories. This makes the initialization both more efficient and easier to optimize. The resulting pipeline, \ours, surpasses the SOTA 4-step chunk-wise Causal Forcing under the \textit{\textbf{frame-wise 2-step setting}} by 0.1 in VBench Total, 0.3 in VBench Quality, and 0.335 in VisionReward, while reducing first-frame latency by 50\% and Stage 2 training cost by $\sim$$4\times$. We further extend the pipeline to action-conditioned world model generation in the spirit of Genie3. Project Page: https://github.com/thu-ml/Causal-Forcing and https://github.com/shengshu-ai/minWM .

Min Zhao, Bokai Yan, Xue Yang et al.

Recent image diffusion transformers achieve high-fidelity generation, but struggle to generate images beyond these scales, suffering from content repetition and quality degradation. In this work, we present UltraImage, a principled framework that addresses both issues. Through frequency-wise analysis of positional embeddings, we identify that repetition arises from the periodicity of the dominant frequency, whose period aligns with the training resolution. We introduce a recursive dominant frequency correction to constrain it within a single period after extrapolation. Furthermore, we find that quality degradation stems from diluted attention and thus propose entropy-guided adaptive attention concentration, which assigns higher focus factors to sharpen local attention for fine detail and lower ones to global attention patterns to preserve structural consistency. Experiments show that UltraImage consistently outperforms prior methods on Qwen-Image and Flux (around 4K) across three generation scenarios, reducing repetition and improving visual fidelity. Moreover, UltraImage can generate images up to 6K*6K without low-resolution guidance from a training resolution of 1328p, demonstrating its extreme extrapolation capability. Project page is available at \href{https://thu-ml.github.io/ultraimage.github.io/}{https://thu-ml.github.io/ultraimage.github.io/}.

Bokai Yan

In this work we propose a Hybrid method with Deviational Particles (HDP) for a plasma modeled by the inhomogeneous Vlasov-Poisson-Landau system. We split the distribution into a Maxwellian part evolved by a grid based fluid solver and a deviation part simulated by numerical particles. These particles, named deviational particles, could be both positive and negative. We combine the Monte Carlo method proposed in \cite{YC15}, a Particle in Cell method and a Macro-Micro decomposition method \cite{BLM08} to design an efficient hybrid method. Furthermore, coarse particles are employed to accelerate the simulation. A particle resampling technique on both deviational particles and coarse particles is also investigated and improved. The efficiency is significantly improved compared to a PIC-MCC method, especially near the fluid regime.

Yuling Jiao, Yang Wang, Bokai Yan

We study the approximation capacity of deep ReLU recurrent neural networks (RNNs) and explore the convergence properties of nonparametric least squares regression using RNNs. We derive upper bounds on the approximation error of RNNs for Hölder smooth functions, in the sense that the output at each time step of an RNN can approximate a Hölder function that depends only on past and current information, termed a past-dependent function. This allows a carefully constructed RNN to simultaneously approximate a sequence of past-dependent Hölder functions. We apply these approximation results to derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer in regression problem. Our error bounds achieve minimax optimal rate under both exponentially $β$-mixing and i.i.d. data assumptions, improving upon existing ones. Our results provide statistical guarantees on the performance of RNNs.

Yuling Jiao, Yanming Lai, Yang Wang et al.

We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples generated via estimated ODE flow converges to the target distribution in the Wasserstein-2 distance under mild and practical assumptions. Furthermore, we show that arbitrary smooth functions can be effectively approximated by transformer networks with Lipschitz continuity, which may be of independent interest.

Yuling Jiao, Yanming Lai, Defeng Sun et al.

We explore the approximation capabilities of Transformer networks for Hölder and Sobolev functions, and apply these results to address nonparametric regression estimation with dependent observations. First, we establish novel upper bounds for standard Transformer networks approximating sequence-to-sequence mappings whose component functions are Hölder continuous with smoothness index $γ\in (0,1]$. To achieve an approximation error $\varepsilon$ under the $L^p$-norm for $p \in [1, \infty]$, it suffices to use a fixed-depth Transformer network whose total number of parameters scales as $\varepsilon^{-d_x n / γ}$. This result not only extends existing findings to include the case $p = \infty$, but also matches the best known upper bounds on number of parameters previously obtained for fixed-depth FNNs and RNNs. Similar bounds are also derived for Sobolev functions. Second, we derive explicit convergence rates for the nonparametric regression problem under various $β$-mixing data assumptions, which allow the dependence between observations to weaken over time. Our bounds on the sample complexity impose no constraints on weight magnitudes. Lastly, we propose a novel proof strategy to establish approximation bounds, inspired by the Kolmogorov-Arnold representation theorem. We show that if the self-attention layer in a Transformer can perform column averaging, the network can approximate sequence-to-sequence Hölder functions, offering new insights into the interpretability of self-attention mechanisms.

Min Zhao, Hongzhou Zhu, Yingze Wang et al.

Despite advances, video diffusion transformers still struggle to generalize beyond their training length, a challenge we term video length extrapolation. We identify two failure modes: model-specific periodic content repetition and a universal quality degradation. Prior works attempt to solve repetition via positional encodings, overlooking quality degradation and achieving only limited extrapolation. In this paper, we revisit this challenge from a more fundamental view: attention maps, which directly govern how context influences outputs. We identify that both failure modes arise from a unified cause: attention dispersion, where tokens beyond the training window dilute learned attention patterns. This leads to quality degradation and repetition emerges as a special case when this dispersion becomes structured into periodic attention patterns, induced by harmonic properties of positional encodings. Building on this insight, we propose UltraViCo, a training-free, plug-and-play method that suppresses attention for tokens beyond the training window via a constant decay factor. By jointly addressing both failure modes, we outperform a broad set of baselines largely across models and extrapolation ratios, pushing the extrapolation limit from 2x to 4x. Remarkably, it improves Dynamic Degree and Imaging Quality by 233% and 40.5% over the previous best method at 4x extrapolation. Furthermore, our method generalizes seamlessly to downstream tasks such as controllable video synthesis and editing.

Yuling Jiao, Yanming Lai, Yang Wang et al.

The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the Hölder continuous function class $\mathcal{H}_{Q}^β\left([0,1]^{d\times n},\mathbb{R}^{d\times n}\right)$ by Transformers and constructs several Transformers that can overcome the curse of dimensionality. These Transformers consist of one self-attention layer with one head and the softmax function as the activation function, along with several feedforward layers. For example, to achieve an approximation accuracy of $ε$, if the activation functions of the feedforward layers in the Transformer are ReLU and floor, only $\mathcal{O}\left(\log\frac{1}ε\right)$ layers of feedforward layers are needed, with widths of these layers not exceeding $\mathcal{O}\left(\frac{1}{ε^{2/β}}\log\frac{1}ε\right)$. If other activation functions are allowed in the feedforward layers, the width of the feedforward layers can be further reduced to a constant. These results demonstrate that Transformers have a strong expressive capability. The construction in this paper is based on the Kolmogorov-Arnold Representation Theorem and does not require the concept of contextual mapping, hence our proof is more intuitively clear compared to previous Transformer approximation works. Additionally, the translation technique proposed in this paper helps to apply the previous approximation results of feedforward neural networks to Transformer research.

Alina Chertock, Changhui Tan, Bokai Yan

We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors and prove that the rescaled solution does not have a singular limit, under appropriate spatial non-oscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, efficiency and asymptotic preserving property of the schemes.