Despite strong performances on many generative tasks, diffusion and flow matching models require a large number of sampling steps to generate high-quality images. This has motivated the community to develop effective methods to distill pre-trained models into more efficient models. In this paper, we present Implicit Generator Matching (IGM), a systematic approach to distill both pre-trained diffusion/flow matching models into one-step generator models, while maintaining almost the same sample generation ability as the original model, as well as being data-free with no need for training images. The key challenge is that the traditional diffusion/flow-matching loss is intractable to distill a teacher diffusion/flow model with an explicitly defined field into a student generator, whose field is defined implicitly. The main breakthrough, our Implicit Gradient Theorem, provides an exact and efficient gradient to directly optimize the student by aligning this implicit field with the teacher's. IGM shows strong empirical performance for one-step generators, setting new standards. On CIFAR10, our diffusion-based SIM achieves an FID score of 2.06, while flow-based FGM sets a flow-model record with a 3.08 FID. Scaling to text-to-image models, SIM distillation of PixArt-$\alpha$α yields a leading 6.42 aesthetic score, surpassing SDXL-TURBO (5.33), and FGM distillation of SD3 achieves a competitive 0.65 GenEval score against multi-step accelerators like Hyper-SD3 (0.63).

Diffusion and flow matching models have achieved remarkable success in text-to-image generation. However, these models typically rely on the predetermined denoising schedules for all prompts. The multi-step reverse diffusion process can be regarded as a kind of chain-of-thought for generating high-quality images step by step. Therefore, diffusion models should reason for each instance to determine the optimal noise schedule adaptively, achieving high generation quality with sampling efficiency. In this paper, we introduce the Time Prediction Diffusion Model (TPDM) for this. TPDM employs a plug-and-play Time Prediction Module (TPM) that predicts the next noise level based on current latent features at each denoising step. We train the TPM using reinforcement learning to maximize a reward that encourages high final image quality while penalizing excessive denoising steps. With such an adaptive scheduler, TPDM not only generates high-quality images that are aligned closely with human preferences but also adjusts diffusion time and the number of denoising steps on the fly, enhancing both performance and efficiency. With Stable Diffusion 3 Medium architecture, TPDM achieves an aesthetic score of 5.44 and a human preference score (HPS) of 29.59, while using around 50% fewer denoising steps to achieve better performance.

We introduce the Diffusion Chain of Lateral Thought (DCoLT), a reasoning framework for diffusion language models. DCoLT treats each intermediate step in the reverse diffusion process as a latent "thinking" action and optimizes the entire reasoning trajectory to maximize the reward on the correctness of the final answer with outcome-based Reinforcement Learning (RL). Unlike traditional Chain-of-Thought (CoT) methods that follow a causal, linear thinking process, DCoLT allows bidirectional, non-linear reasoning with no strict rule on grammatical correctness amid its intermediate steps of thought. We implement DCoLT on two representative Diffusion Language Models (DLMs). First, we choose SEDD as a representative continuous-time discrete diffusion model, where its concrete score derives a probabilistic policy to maximize the RL reward over the entire sequence of intermediate diffusion steps. We further consider the discrete-time masked diffusion language model -- LLaDA, and find that the order to predict and unmask tokens plays an essential role to optimize its RL action resulting from the ranking-based Unmasking Policy Module (UPM) defined by the Plackett-Luce model. Experiments on both math and code generation tasks show that using only public data and 16 H800 GPUs, DCoLT-reinforced DLMs outperform other DLMs trained by SFT or RL or even both. Notably, DCoLT-reinforced LLaDA boosts its reasoning accuracy by +9.8%, +5.7%, +11.4%, +19.5% on GSM8K, MATH, MBPP, and HumanEval.

Despite their strong performances on many generative tasks, diffusion models require a large number of sampling steps in order to generate realistic samples. This has motivated the community to develop effective methods to distill pre-trained diffusion models into more efficient models, but these methods still typically require few-step inference or perform substantially worse than the underlying model. In this paper, we present Score Implicit Matching (SIM) a new approach to distilling pre-trained diffusion models into single-step generator models, while maintaining almost the same sample generation ability as the original model as well as being data-free with no need of training samples for distillation. The method rests upon the fact that, although the traditional score-based loss is intractable to minimize for generator models, under certain conditions we \emph{can} efficiently compute the \emph{gradients} for a wide class of score-based divergences between a diffusion model and a generator. SIM shows strong empirical performances for one-step generators: on the CIFAR10 dataset, it achieves an FID of 2.06 for unconditional generation and 1.96 for class-conditional generation. Moreover, by applying SIM to a leading transformer-based diffusion model, we distill a single-step generator for text-to-image (T2I) generation that attains an aesthetic score of 6.42 with no performance decline over the original multi-step counterpart, clearly outperforming the other one-step generators including SDXL-TURBO of 5.33, SDXL-LIGHTNING of 5.34 and HYPER-SDXL of 5.85. We will release this industry-ready one-step transformer-based T2I generator along with this paper.