Jaemoo Choi

Jaemoo Choi, Yesom Park, Myungjoo Kang

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

Yesom Park, Jaemoo Choi, Changyeon Yoon et al.

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make specific assumptions on the type of DEs, making the model specialized for particular problems. This work presents a partial differential equation (PDE) based framework which improves the dynamics modeling capability. Building upon the recent Fourier neural operator, we propose a neural operator that can handle time continuously without requiring iterative operations or specific grids of temporal discretization. A theoretical result demonstrating its universality is provided. We also uncover an intrinsic property of neural operators that improves data efficiency and model generalization by ensuring stability. Our model achieves superior accuracy in dealing with time-dependent PDEs compared to existing models. Furthermore, several numerical pieces of evidence validate that our method better represents a wide range of dynamics and outperforms state-of-the-art DE-based models in real-time-series applications. Our framework opens up a new way for a continuous representation of neural networks that can be readily adopted for real-world applications.

Yuchen Zhu, Wei Guo, Jaemoo Choi et al.

Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is a crucial component for dLLMs to achieve comparable performance with AR-LLMs on important tasks, such as reasoning. However, RL algorithms that are well-suited for dLLMs' unique characteristics have yet to be developed. This paper proposes Distribution Matching Policy Optimization (DMPO), a principled and theoretically grounded RL fine-tuning method specifically designed to enhance the reasoning capabilities of dLLMs by matching the dLLM policy distribution to the optimal, reward-tilted one through cross-entropy optimization. We identify a key challenge in the implementation with a small training batch size and propose several effective solutions through a novel weight baseline subtraction technique. DMPO exhibits superior performance on multiple reasoning benchmarks without supervised fine-tuning, with an accuracy improvement of up to $42.9\%$ over previously SOTA baselines and $55.8\%$ over the base model, underscoring the effectiveness of the distribution matching framework. Our code is available at https://github.com/yuchen-zhu-zyc/DMPO.

Jaemoo Choi, Jaewoong Choi, Myungjoo Kang

Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a given cost function. In this regard, OT between tractable prior distribution and data has been utilized for generative modeling tasks. However, OT-based methods are susceptible to outliers and face optimization challenges during training. In this paper, we propose a novel generative model based on the semi-dual formulation of Unbalanced Optimal Transport (UOT). Unlike OT, UOT relaxes the hard constraint on distribution matching. This approach provides better robustness against outliers, stability during training, and faster convergence. We validate these properties empirically through experiments. Moreover, we study the theoretical upper-bound of divergence between distributions in UOT. Our model outperforms existing OT-based generative models, achieving FID scores of 2.97 on CIFAR-10 and 6.36 on CelebA-HQ-256. The code is available at \url{https://github.com/Jae-Moo/UOTM}.

Jaemoo Choi, Jaewoong Choi, Myungjoo Kang

Wasserstein Gradient Flow (WGF) describes the gradient dynamics of probability density within the Wasserstein space. WGF provides a promising approach for conducting optimization over the probability distributions. Numerically approximating the continuous WGF requires the time discretization method. The most well-known method for this is the JKO scheme. In this regard, previous WGF models employ the JKO scheme and parametrize transport map for each JKO step. However, this approach results in quadratic training complexity $O(K^2)$ with the number of JKO step $K$. This severely limits the scalability of WGF models. In this paper, we introduce a scalable WGF-based generative model, called Semi-dual JKO (S-JKO). Our model is based on the semi-dual form of the JKO step, derived from the equivalence between the JKO step and the Unbalanced Optimal Transport. Our approach reduces the training complexity to $O(K)$. We demonstrate that our model significantly outperforms existing WGF-based generative models, achieving FID scores of 2.62 on CIFAR-10 and 5.46 on CelebA-HQ-256, which are comparable to state-of-the-art image generative models.

Jaemoo Choi, Yongxin Chen, Molei Tao et al.

Recently, there has been significant progress in learning-based diffusion samplers, which aim to sample from a given unnormalized density. These methods typically follow one of two paradigms: (i) formulating sampling as an unbiased stochastic optimal control (SOC) problem using a canonical reference process, or (ii) refining annealed path measures through importance-weighted sampling. Although annealing approaches have advantages in guiding samples toward high-density regions, reliance on importance sampling leads to high variance and limited scalability in practice. In this paper, we introduce the \textbf{Non-equilibrium Annealed Adjoint Sampler (NAAS)}, a novel SOC-based diffusion sampler that leverages annealed reference dynamics without resorting to importance sampling. NAAS employs a lean adjoint system inspired by adjoint matching, enabling efficient and scalable training. We demonstrate the effectiveness of our approach across a range of tasks, including sampling from classical energy landscapes and molecular Boltzmann distribution.

Wei Guo, Jaemoo Choi, Yuchen Zhu et al. · gatech

The task of learning a diffusion-based neural sampler for drawing samples from an unnormalized target distribution can be viewed as a stochastic optimal control problem on path measures. However, the training of neural samplers can be challenging when the target distribution is multimodal with significant barriers separating the modes, potentially leading to mode collapse. We propose a framework named \textbf{Proximal Diffusion Neural Sampler (PDNS)} that addresses these challenges by tackling the stochastic optimal control problem via proximal point method on the space of path measures. PDNS decomposes the learning process into a series of simpler subproblems that create a path gradually approaching the desired distribution. This staged procedure traces a progressively refined path to the desired distribution and promotes thorough exploration across modes. For a practical and efficient realization, we instantiate each proximal step with a proximal weighted denoising cross-entropy (WDCE) objective. We demonstrate the effectiveness and robustness of PDNS through extensive experiments on both continuous and discrete sampling tasks, including challenging scenarios in molecular dynamics and statistical physics.

Jaemoo Choi, Jaewoong Choi, Dohyun Kwon

We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning OT Maps with neural networks, often generates spurious solutions that fail to transfer one distribution to another accurately. We identify a sufficient condition under which the max-min solution of Semi-dual Neural OT recovers the true OT Map. Moreover, to address cases when this sufficient condition is not satisfied, we propose a novel method, OTP, which learns both the OT Map and the Optimal Transport Plan, representing the optimal coupling between two distributions. Under sharp assumptions on the distributions, we prove that our model eliminates the spurious solution issue and correctly solves the OT problem. Our experiments show that the OTP model recovers the optimal transport map where existing methods fail and outperforms current OT-based models in image-to-image translation tasks. Notably, the OTP model can learn stochastic transport maps when deterministic OT Maps do not exist, such as one-to-many tasks like colorization.