Pipi Hu

Jingyuan Li, Xiaoyi Jiang, Fukang Wen et al. · microsoft-research

Discrete diffusion models based on continuous-time Markov chains (CTMCs) have shown strong performance on language and discrete data generation, yet existing approaches typically parameterize the reverse rate matrix as a single object -- via concrete scores, clean-data predictions ($x_0$-parameterization), or denoising distributions -- rather than aligning the parameterization with the intrinsic CTMC decomposition into jump timing and jump direction. Since a CTMC is fundamentally a Poisson process fully determined by these two quantities, decomposing along this structure is closer to first principles and naturally leads to our formulation. We propose \textbf{Neural CTMC}, which separately parameterizes the reverse process through an \emph{exit rate} (when to jump) and a \emph{jump distribution} (where to jump) using two dedicated network heads. We show that the evidence lower bound (ELBO) differs from a path-space KL divergence between the true and learned reverse processes by a $θ$-independent constant, so that the training objective is fully governed by the exit rate and jump distribution we parameterize. Moreover, this KL factorizes into a Poisson KL for timing and a categorical KL for direction. We further show that the tractable conditional surrogate preserves the gradients and minimizers of the corresponding marginal reverse-process objective under standard regularity assumptions. Our theoretical framework also covers masked and GIDD-style noise schedules. Empirically, while the uniform forward process has been explored in prior work, our model, to our best of the knowledge, is the first pure-uniform method to outperform mask-based methods on the OpenWebText dataset.To facilitate reproducibility, we release our pretrained weights at https://huggingface.co/Jiangxy1117/Neural-CTMC.

Guochang Lin, Fukai Chen, Pipi Hu et al.

Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following three folds. Firstly, compared with the original PDE, the dimension of Green's function is doubled, making it impossible to be handled by traditional mesh-based methods. Secondly, Green's function usually contains singularities which increase the difficulty to get a good approximation. Lastly, the computational domain may be very complex or even unbounded. To override these problems, we leverage the fundamental solution, boundary integral method and neural networks to develop a new method for computing Green's function with high accuracy in this paper. We focus on Green's function of Poisson and Helmholtz equations in bounded domains, unbounded domains. We also consider Poisson equation and Helmholtz domains with interfaces. Extensive numerical experiments illustrate the efficiency and the accuracy of our method for solving Green's function. In addition, we also use the Green's function calculated by our method to solve a class of PDE, and also obtain high-precision solutions, which shows the good generalization ability of our method on solving PDEs.

Liwei Lu, Zhijun Zeng, Yan Jiang et al.

Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many scenarios. Here we present an approach to effectively modeling the dynamics of the stochastic data without trajectories based on the weak form of the Fokker-Planck (FP) equation, which governs the evolution of the density function in the Brownian process. Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data. With a dictionary representation of the unknown terms, a linear system is built and then solved by the regression, revealing the unknown dynamics of the data. Hence, we name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression. The numerical experiments show that our method is flexible and fast, which reveals the dynamics within seconds in multi-dimensional problems and can be easily extended to high-dimensional data such as 20 dimensions. WCR can also correctly identify the hidden dynamics of the complex tasks with variable-dependent diffusion and coupled drift, and the performance is robust, achieving high accuracy in the case with noise added.

Zhijun Zeng, Yixuan Jiang, Pipi Hu et al.

Density estimation is a central primitive in probabilistic modeling, yet continuous, discrete, and mixed-variable domains are often treated by separate objectives, limiting the ability to exploit a common statistical structure across data types. Continuous score-based methods rely on log-density gradients, while discrete extensions typically use concrete score whose unbounded targets become unstable near low-probability states. We introduce Constant-Target Energy Matching (CTEM), a unified energy-based framework for density estimation on general state spaces. CTEM replaces ordinary density-ratio regression with a bounded energy-difference transform and derives from it a sample-only training objective with the constant target 1. The learned scalar potential recovers log p without partition-function estimation or explicit unbounded ratio regression. Across continuous, discrete, and mixed-variable benchmarks, CTEM substantially improves density estimation over competitive baselines and yields higher-quality samples under standard sampling procedures.

Mingqian Ma, Guoqing Liu, Chuan Cao et al. · microsoft-research

Advances in natural language processing and large language models have sparked growing interest in modeling DNA, often referred to as the "language of life". However, DNA modeling poses unique challenges. First, it requires the ability to process ultra-long DNA sequences while preserving single-nucleotide resolution, as individual nucleotides play a critical role in DNA function. Second, success in this domain requires excelling at both generative and understanding tasks: generative tasks hold potential for therapeutic and industrial applications, while understanding tasks provide crucial insights into biological mechanisms and diseases. To address these challenges, we propose HybriDNA, a decoder-only DNA language model that incorporates a hybrid Transformer-Mamba2 architecture, seamlessly integrating the strengths of attention mechanisms with selective state-space models. This hybrid design enables HybriDNA to efficiently process DNA sequences up to 131kb in length with single-nucleotide resolution. HybriDNA achieves state-of-the-art performance across 33 DNA understanding datasets curated from the BEND, GUE, and LRB benchmarks, and demonstrates exceptional capability in generating synthetic cis-regulatory elements (CREs) with desired properties. Furthermore, we show that HybriDNA adheres to expected scaling laws, with performance improving consistently as the model scales from 300M to 3B and 7B parameters. These findings underscore HybriDNA's versatility and its potential to advance DNA research and applications, paving the way for innovations in understanding and engineering the "language of life".

Gongbo Zhang, Yanting Li, Renqian Luo et al. · microsoft-research

Function in natural systems arises from one-dimensional sequences forming three-dimensional structures with specific properties. However, current generative models suffer from critical limitations: training objectives seldom target function directly, discrete sequences and continuous coordinates are optimized in isolation, and conformational ensembles are under-modeled. We present UniGenX, a unified generative foundation model that addresses these gaps by co-generating sequences and coordinates under direct functional and property objectives across proteins, molecules, and materials. UniGenX represents heterogeneous inputs as a mixed stream of symbolic and numeric tokens, where a decoder-only autoregressive transformer provides global context and a conditional diffusion head generates numeric fields steered by task-specific tokens. Besides the new high SOTAs on structure prediction tasks, the model demonstrates state-of-the-art or competitive performance for the function-aware generation across domains: in materials, it achieves "conflicted" multi-property conditional generation, yielding 436 crystal candidates meeting triple constraints, including 11 with novel compositions; in chemistry, it sets new benchmarks on five property targets and conformer ensemble generation on GEOM; and in biology, it improves success in modeling protein induced fit (RMSD < 2 Å) by over 23-fold and enhances EC-conditioned enzyme design. Ablation studies and cross-domain transfer substantiate the benefits of joint discrete-continuous training, establishing UniGenX as a significant advance from prediction to controllable, function-aware generation.

Liya Guo, Liwei Lu, Zhijun Zeng et al.

With the rapid increase of observational, experimental and simulated data for stochastic systems, tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extracting stochastic dynamics with Lévy noise are relatively few. In this work, we propose a Weak Collocation Regression (WCR) to explicitly reveal unknown stochastic dynamical systems, i.e., the Stochastic Differential Equation (SDE) with both $α$-stable Lévy noise and Gaussian noise, from discrete aggregate data. This method utilizes the evolution equation of the probability distribution function, i.e., the Fokker-Planck (FP) equation. With the weak form of the FP equation, the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations. Then, the unknown parameters are obtained by a sparse linear regression. For a SDE with Lévy noise, the corresponding FP equation is a partial integro-differential equation (PIDE), which contains nonlocal terms, and is difficult to deal with. The weak form can avoid complicated multiple integrals. Our approach can simultaneously distinguish mixed noise types, even in multi-dimensional problems. Numerical experiments demonstrate that our method is accurate and computationally efficient.

Liya Guo, Zun Wang, Chang Liu et al.

The ensemble average of physical properties of molecules is closely related to the distribution of molecular conformations, and sampling such distributions is a fundamental challenge in physics and chemistry. Traditional methods like molecular dynamics (MD) simulations and Markov chain Monte Carlo (MCMC) sampling are commonly used but can be time-consuming and costly. Recently, diffusion models have emerged as efficient alternatives by learning the distribution of training data. Obtaining an unbiased target distribution is still an expensive task, primarily because it requires satisfying ergodicity. To tackle these challenges, we propose Potential Score Matching (PSM), an approach that utilizes the potential energy gradient to guide generative models. PSM does not require exact energy functions and can debias sample distributions even when trained on limited and biased data. Our method outperforms existing state-of-the-art (SOTA) models on the Lennard-Jones (LJ) potential, a commonly used toy model. Furthermore, we extend the evaluation of PSM to high-dimensional problems using the MD17 and MD22 datasets. The results demonstrate that molecular distributions generated by PSM more closely approximate the Boltzmann distribution compared to traditional diffusion models.

Pipi Hu

Perturbation and operator adjoint method are used to give the right adjoint form rigourously. From the derivation, we can have following results: 1) The loss gradient is not an ODE, it is an integral and we shows the reason; 2) The traditional adjoint form is not equivalent with the back propagation results. 3) The adjoint operator analysis shows that if and only if the discrete adjoint has the same scheme with the discrete neural ODE, the adjoint form would give the same results as BP does.

Zhijun Zeng, Pipi Hu, Chenglong Bao et al.

In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.

Pipi Hu, Wuyue Yang, Yi Zhu et al.

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation network (ODENet), in which the numerical integration of explicit ordinary differential equations (ODEs) are embedded into the machine learning scheme to build a general framework for revealing the hidden dynamics buried in massive time-series data efficiently and reliably. ODENet takes full advantage of both machine learning algorithms and ODE modeling. On one hand, the embedding of ODEs makes the framework more interpretable benefiting from the mature theories of ODEs. On the other hand, the schemes of machine learning enable data handling, paralleling, and optimization to be easily and efficiently implemented. From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet exhibits its remarkable capability in handling time-series data even in the presence of large noise. We further apply the ODENet to real actin aggregation data, which shows an impressive performance as well. These results demonstrate the superiority of ODENet in dealing with noisy data, data with either non-equal spacing or large sampling time steps over other traditional machine learning algorithms.