A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models
Introduces a continuous-time RL framework to optimize discrete diffusion models, enhancing performance in reasoning and coding tasks.
Key Findings
Methodology
This paper presents a continuous-time reinforcement learning framework, integrating control theory with policy optimization in discrete state spaces. By introducing continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO), it enables reward-driven optimization of score-based discrete diffusion models.
Key Results
- Achieved 88.2% accuracy on Sudoku, demonstrating strong effectiveness in reasoning and coding tasks.
- PPO algorithm outperformed alternatives in generation performance and convergence on low-dimensional synthetic data.
- In LLaDA experiments, CTRL demonstrated strong effectiveness in mathematical reasoning tasks (Sudoku, GSM8K, MATH500) and coding tasks (HumanEval, MBPP).
Significance
This research provides a new perspective for fine-tuning discrete diffusion models, addressing challenges in handling non-differentiable reward signals. It has significant implications for academia and offers new possibilities for text generation and language model optimization in industry.
Technical Contribution
The paper introduces a novel continuous-time RL framework in discrete state spaces, combining control theory with RL policy optimization, providing new theoretical guarantees and engineering possibilities. Trajectory subsampling techniques reduce computational costs for per-position probability ratios.
Novelty
This is the first application of a continuous-time RL framework in discrete state spaces, solving optimization challenges with non-differentiable reward signals, offering significant innovations compared to existing GRPO methods.
Limitations
- High computational cost in high-dimensional tasks may affect real-time applications.
- The framework requires careful design of reward models, potentially limiting effectiveness in certain applications.
Future Work
Future work could explore applications in other types of discrete diffusion models and further optimize computational efficiency.
AI Executive Summary
This study introduces a continuous-time reinforcement learning framework for optimizing discrete diffusion models, particularly masked diffusion large language models (dLLMs). Existing methods struggle with non-differentiable reward signals, while this paper achieves reward-driven optimization through continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO).
The framework allows intermediate reward signals to be integrated throughout the denoising trajectory, especially in masked diffusion models (MDMs), providing a unified perspective on exploration and policy optimization. Trajectory subsampling techniques reduce computational costs for per-position probability ratios, demonstrating strong effectiveness in reasoning and coding tasks.
Despite its strong performance in experiments, high computational cost remains a challenge in high-dimensional tasks. Future work could explore further optimization of computational efficiency and applications in other types of discrete diffusion models.
Deep Analysis
Background
In recent years, diffusion models have made significant progress in image generation and are gradually being applied to discrete data generation. Discrete diffusion models use continuous-time Markov chains (CTMC) to model state dynamics, becoming powerful tools for generating text with large language models (LLMs). However, existing methods struggle with non-differentiable reward signals, limiting their application in reinforcement learning fine-tuning.
Core Problem
Fine-tuning discrete diffusion models is challenging because sampling from discrete categorical distributions is non-differentiable, making standard gradient methods inapplicable. Specifically, in language models, traditional autoregressive methods struggle to scale and enhance dLLMs' reasoning capabilities due to the intractable likelihood of generated sequences in any-order decoding.
Innovation
This paper proposes a continuous-time reinforcement learning framework, integrating control theory with policy optimization in discrete state spaces. By introducing continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO), it enables reward-driven optimization of score-based discrete diffusion models. Trajectory subsampling techniques reduce computational costs for per-position probability ratios.
Methodology
- �� Model state dynamics using continuous-time Markov chains (CTMC)
- �� Introduce proximal policy optimization (PPO) and group relative policy optimization (GRPO)
- �� Use trajectory subsampling techniques to reduce computational costs
- �� Integrate intermediate reward signals in masked diffusion models (MDMs)
Experiments
Experiments were conducted on low-dimensional synthetic data and the open-sourced 8B dLLM (LLaDA) for reasoning and coding tasks. The effectiveness of the proposed methods was validated by comparing generation performance and convergence of different algorithms.
Results
Achieved 88.2% accuracy on Sudoku, demonstrating strong effectiveness in reasoning and coding tasks. PPO algorithm outperformed alternatives in generation performance and convergence on low-dimensional synthetic data.
Applications
The framework can be used to optimize text generation in large language models, particularly in scenarios requiring complex reasoning tasks. It offers new possibilities for text generation and language model optimization in industry.
Limitations & Outlook
High computational cost in high-dimensional tasks may affect real-time applications. The framework requires careful design of reward models, potentially limiting effectiveness in certain applications.
Plain Language Accessible to non-experts
Imagine you're cooking in a kitchen. You have a recipe, but each step needs to be adjusted based on the actual situation. Continuous-time reinforcement learning is like constantly adjusting the seasoning and heat to achieve the best taste. Discrete diffusion models are like different ingredients that need to be processed at specific time points. By continuously adjusting and optimizing, you can end up with a delicious dish.
ELI14 Explained like you're 14
Imagine you're playing a game where each level has different challenges. You need to constantly adjust your strategy to pass the levels. Continuous-time reinforcement learning is like adjusting your game strategy to achieve better scores. Discrete diffusion models are like different game items that need to be used at specific times. By continuously optimizing your strategy, you can achieve higher scores in the game!
Glossary
Continuous-Time Markov Chain (CTMC)
A mathematical model used to describe systems whose states change over time, with transitions governed by probabilities.
Used to model state dynamics in discrete diffusion models.
Proximal Policy Optimization (PPO)
A reinforcement learning algorithm that stabilizes training by limiting the magnitude of policy updates.
Used for optimizing policies in discrete diffusion models.
Group Relative Policy Optimization (GRPO)
A reinforcement learning algorithm that optimizes using relative advantages of group policies.
Used for fine-tuning discrete diffusion models.
Trajectory Subsampling
A technique to reduce computational costs by selectively sampling trajectories to estimate probabilities.
Used to lower costs for computing per-position probability ratios.
Masked Diffusion Model (MDM)
A diffusion model that processes data with masks and predicts clean data.
Applied in discrete diffusion models.
Open Questions Unanswered questions from this research
- 1 How to further reduce computational costs in high-dimensional tasks?
- 2 How to design more effective reward models for different application scenarios?
Applications
Immediate Applications
Text Generation Optimization
The framework can be used to optimize text generation in large language models, especially in scenarios requiring complex reasoning tasks.
Long-term Vision
Intelligent Dialogue Systems
By optimizing language models, improve response quality and reasoning capabilities of intelligent dialogue systems.
Abstract
We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC). We consider policy optimization problems and derive the corresponding policy gradient methods, leading to continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO). As a primary application, we develop a complete continuous-time RL framework for fine-tuning score-based discrete diffusion models. The proposed framework enables reward-driven optimization without requiring differentiability on the reward signals. In contrast to the existing GRPO-based approaches that only rely on terminal rewards, our formulation allows intermediate reward or advantage signals to be incorporated throughout the denoising trajectory. Importantly, when specialized to masked diffusion models (MDMs), our framework encompasses a rich class of policy parameterizations over the vocabulary simplex with analytically tractable probability ratios, providing a unified perspective on exploration and policy optimization in MDMs. For masked diffusion large language models (dLLMs), we further propose trajectory subsampling techniques to efficiently estimate computationally prohibitive trajectory likelihoods, reducing the computational cost of computing per-position probability ratios. We showcase the effectiveness of our methods on both low-dimensional entropy-regularized optimization problems and RL post-training of dLLMs on mathematical reasoning and coding tasks.