Low-Rank Adaptation (LoRA) has emerged as a widely adopted technique in text-to-image models, enabling precise rendering of multiple distinct elements, such as characters and styles, in multi-concept image generation. However, current approaches face significant challenges when composing these LoRAs for multi-concept image generation, particularly as the number of LoRAs increases, resulting in diminished generated image quality. In this paper, we initially investigate the role of LoRAs in the denoising process through the lens of the Fourier frequency domain. Based on the hypothesis that applying multiple LoRAs could lead to "semantic conflicts", we have conducted empirical experiments and find that certain LoRAs amplify high-frequency features such as edges and textures, whereas others mainly focus on low-frequency elements, including the overall structure and smooth color gradients. Building on these insights, we devise a frequency domain based sequencing strategy to determine the optimal order in which LoRAs should be integrated during inference. This strategy offers a methodical and generalizable solution compared to the naive integration commonly found in existing LoRA fusion techniques. To fully leverage our proposed LoRA order sequence determination method in multi-LoRA composition tasks, we introduce a novel, training-free framework, Cached Multi-LoRA (CMLoRA), designed to efficiently integrate multiple LoRAs while maintaining cohesive image generation. With its flexible backbone for multi-LoRA fusion and a non-uniform caching strategy tailored to individual LoRAs, CMLoRA has the potential to reduce semantic conflicts in LoRA composition and improve computational efficiency. Our experimental evaluations demonstrate that CMLoRA outperforms state-of-the-art training-free LoRA fusion methods by a significant margin -- it achieves an average improvement of $2.19$% in CLIPScore, and $11.25%$% in MLLM win rate compared to LoraHub, LoRA Composite, and LoRA Switch.

Aligning Large Language Model (LLM) responses with human preferences is vital for building safe and controllable AI systems. While preference optimization methods based on Plackett-Luce (PL) and Bradley-Terry (BT) models have shown promise, they face challenges such as poor handling of harmful content, inefficient use of dispreferred responses, and, specifically for PL, high computational costs. To address these issues, we propose Hard Preference Sampling (HPS), a novel framework for robust and efficient human preference alignment. HPS introduces a training loss that prioritizes the most preferred response while rejecting all dispreferred and harmful ones. It emphasizes “hard” dispreferred responses — those closely resembling preferred ones — to enhance the model’s rejection capabilities. By leveraging a single-sample Monte Carlo sampling strategy, HPS reduces computational overhead while maintaining alignment quality. Theoretically, HPS improves sample efficiency over existing PL methods and maximizes the reward margin between preferred and dispreferred responses, ensuring clearer distinctions. Experiments on HH-RLHF and PKU-Safety datasets validate HPS’s effectiveness, achieving comparable BLEU and reward scores while greatly improving reward margins and thus reducing harmful content generation.