Post-training of large language models involves a fundamental trade-off between supervised fine-tuning (SFT), which efficiently mimics demonstrations but tends to memorize, and reinforcement learning (RL), which achieves better generalization at higher computational cost. Dynamic Fine-Tuning (DFT) recently emerged as a promising middle ground, reweighting SFT objectives with token probabilities and achieving improvements in certain reasoning domains, though it exhibits instability in other tasks. We provide a analysis of DFT through the reward-weighted regression (RWR) framework, revealing that it corresponds to a specific auxiliary distribution choice that yields provably tighter RL bounds than standard SFT. However, our analysis also uncovers a critical limitation: this construction lacks distributional anchoring, leading to progressive drift that undermines training stability. To address this, we propose Anchored Supervised Fine-T uning (ASFT), which augments DFT's reweighting with lightweight KL regularization to preserve tightness while ensuring stability. Empirically, ASFT consistently outperforms both SFT and DFT across mathematical reasoning, medical knowledge grounding, and code generation, achieving substantial improvements with minimal computational overhead. Our RWR framework provides a systematic lens for understanding post-training methods and demonstrates that principled theoretical analysis leads to both stronger guarantees and practical gains. Large language models (LLMs) have become a central substrate for modern AI systems, powering instruction following, tool use, and multi-step reasoning at scale (Brown et al., 2020; Touvron et al., 2023; Achiam et al., 2023; Guo et al., 2025).

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on unstructured data like 3D point clouds. These models are commonly trained in two stages: first, a data compressor (i.e. a variational auto-encoder) is trained, and in a subsequent training stage a flow matching generative model is trained in the low-dimensional latent space of the data compressor. This two stage paradigm adds complexity to the overall training recipe and sets obstacles for unifying models across data domains, as specific data compressors are used for different data modalities. To this end, we introduce Ambient Space Flow Transformers (ASFT), a domain-agnostic approach to learn flow matching transformers in ambient space, sidestepping the requirement of training compressors and simplifying the training process. We introduce a conditionally independent point-wise training objective that enables ASFT to make predictions continuously in coordinate space. Our empirical results demonstrate that using general purpose transformer blocks, ASFT effectively handles different data modalities such as images and 3D point clouds, achieving strong performance in both domains and outperforming comparable approaches. ASFT is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains. Recent advances in generative modeling have enabled learning complex data distributions by combining both powerful architectures and training objectives. In particular, state-of-the-art approaches for image (Esser et al., 2024), video (Dai et al., 2023) or 3D point cloud (Vahdat et al., 2022) generation are based on the concept of iteratively transforming data into Gaussian noise. Diffusion models were originally proposed following this idea and pushing the quality of generated samples in many different domains, including images (Dai et al., 2023; Rombach et al., 2022), 3D point clouds (Luo & Hu, 2021), graphs (Hoogeboom et al., 2022) and video (Ho et al., 2022a). More recently, flow matching (Lipman et al., 2023) and stochastic interpolants (Ma et al., 2024) have been proposed as generalized formulations of the noising process, moving from stochastic gaussian diffusion processes to general paths connecting a base (e.g.

Direct Preference Optimization (DPO) is a method for enhancing model performance by directly optimizing for the preferences or rankings of outcomes, instead of traditional loss functions. This approach has proven effective in aligning Large Language Models (LLMs) with human preferences. Despite its widespread use across various tasks, DPO has been criticized for its sensitivity to the effectiveness of Supervised Fine-Tuning (SFT) and its limitations in enabling models to learn human-preferred responses, leading to less satisfactory performance. To address these limitations, we propose Aligned Supervised Fine-Tuning (ASFT), an effective approach that better aligns LLMs with pair-wise datasets by optimizing absolute likelihood for each response, rather than using the Bradley-Terry model, and eliminates the need for a reference model. Through theoretical gradient analysis, we demonstrate that ASFT mitigates the issue where the DPO loss function decreases the probability of generating human-dispreferred data at a faster rate than it increases the probability of producing preferred data. Additionally, we compare ASFT to DPO and its latest variants, such as the single-step approach ORPO, using the latest instruction-tuned model Llama3, which has been fine-tuned on UltraFeedback and HH-RLHF. We evaluated performance on instruction-following benchmarks like MT-Bench and traditional text generation metrics such as BLEU-4 and ROUGE-L. Extensive experiments demonstrate that ASFT is an effective alignment approach, consistently outperforming existing methods.