Stabilizing Consistency Training: A Flow Map Analysis and Self-Distillation

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

Semi-gradient DICE for Offline Constrained Reinforcement Learning

Stationary Distribution Correction Estimation (DICE) addresses the mismatch between the stationary distribution induced by a policy and the target distribution required for reliable off-policy evaluation (OPE) and policy optimization. DICE-based offline constrained RL particularly benefits from the flexibility of DICE, as it simultaneously maximizes return while estimating costs in offline settings. However, we have observed that recent approaches designed to enhance the offline RL performance of the DICE framework inadvertently undermine its ability to perform OPE, making them unsuitable for constrained RL scenarios. In this paper, we identify the root cause of this limitation: their reliance on a semi-gradient optimization, which solves a fundamentally different optimization problem and results in failures in cost estimation. Building on these insights, we propose a novel method to enable OPE and constrained RL through semi-gradient DICE. Our method ensures accurate cost estimation and achieves state-of-the-art performance on the offline constrained RL benchmark, DSRL.

FairDICE: Fairness-Driven Offline Multi-Objective Reinforcement Learning

Multi-objective reinforcement learning (MORL) aims to optimize policies in the presence of conflicting objectives, where linear scalarization is commonly used to reduce vector-valued returns into scalar signals. While effective for certain preferences, this approach cannot capture fairness-oriented goals such as Nash social welfare or max-min fairness, which require nonlinear and non-additive trade-offs. Although several online algorithms have been proposed for specific fairness objectives, a unified approach for optimizing nonlinear welfare criteria in the offline setting-where learning must proceed from a fixed dataset-remains unexplored. In this work, we present FairDICE, the first offline MORL framework that directly optimizes nonlinear welfare objective. FairDICE leverages distribution correction estimation to jointly account for welfare maximization and distributional regularization, enabling stable and sample-efficient learning without requiring explicit preference weights or exhaustive weight search. Across multiple offline benchmarks, FairDICE demonstrates strong fairness-aware performance compared to existing baselines.