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Applications · Everything Else

Ziheng Ni, Congcong Liu, Yuying Chen, Zhiwei Fang, Changping Peng, Zhangang Lin, Ching Law, Jingping Shao

Click-through rate (CTR) prediction is crucial for recommendation systems and online advertising, relying heavily on effective user behavior modeling. While existing methods separately refine long-term and short-term interest representations, the fusion of these behaviors remains a critical yet understudied challenge due to misaligned feature spaces, disjointed modeling, and noise propagation in short-term interests. To address these limitations, we propose iFusion, a diffusion-based generative user interest fusion method, which reformulates interest fusion as a conditional generation process. iFusion leverages short-term interests as conditional guidance and progressively integrates long-term representations through denoising, eliminating reliance on linear fusion assumptions. Our framework introduces two key components: (1) the Disentangled Classifier-Free Diffusion Guidance (DCFG) Mechanism, which adaptively disentangles core preferences from transient fluctuations, and (2) the Mixture AutoRegressive Denoising Network (MARN), which enables joint interest modeling and fusion through autoregressive denoising. Experiments demonstrate that iFusion outperforms baselines across public and industrial datasets, as well as in online A/B tests, validating its effectiveness in robust CTR prediction. This work establishes a new paradigm for generative user interests fusion in CTR prediction.

Deep Learning · Generative Models and Autoencoders

Debottam Dutta, Jianchong Chen, Rajalaxmi Rajagopalan, Yu-Lin Wei, Romit Roy Choudhury

We propose to improve multi-concept prompt fidelity in text-to-image diffusion models. We begin with common failure cases—prompts like “a cat and a dog” that sometimes yields images where one concept is missing, faint, or colliding awkwardly with another. We hypothesize that this happens when the diffusion model drifts into mixed modes that over-emphasize a single concept it learned strongly during training. Instead of re-training, we introduce a corrective sampling strategy that steers away from regions where the joint prompt behavior overlaps too strongly with any single concept in the prompt. The goal is to steer towards “pure” joint modes where all concepts can coexist with balanced visual presence. We further show that existing multi-concept guidance schemes can operate in unstable weight regimes that amplify imbalance; we characterize favorable regions and adapt sampling to remain within them. Our approach, CO3, is plug-and-play, requires no model tuning, and complements standard classifier-free guidance. Experiments on diverse multi-concept prompts indicate improvements in concept coverage, balance and robustness, with fewer dropped or distorted concepts compared to standard baselines and prior compositional methods. Results suggest that lightweight corrective guidance can substantially mitigate brittle semantic alignment behavior in modern diffusion systems. Code is available at https://github.com/debottam-dutta7/co3

Deep Learning · Generative Models and Autoencoders

Rafał Karczewski, Markus Heinonen, Alison Pouplin, Søren Hauberg, Vikas Garg

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of $\mathbf{x}_T$ as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime $\mathbf{z}=(\mathbf{x}_t,t)$ that indexes the family of denoising distributions $p(\mathbf{x}_0 | \mathbf{x}_t)$ across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Applications · Robotics

Chengyang He, Xu Liu, Gadiel Sznaier Camps, Joseph Bruno, Guillaume Sartoretti, Mac Schwager

Diffusion policies for visuomotor robot manipulation tasks achieve remarkable dexterity and robustness while only training on a small number of task demonstrations. However, the reason for this performance remains a mystery. In this paper, we offer a surprising hypothesis: diffusion policies essentially memorize an action lookup table---\emph{and this is beneficial}. We posit that, at runtime, diffusion policies find the closest training image to the test image in a latent space, and recall the associated training action (i.e. action chunk), offering reactivity without the need for action generalization. This is effective in the sparse data regime, where there is not enough data density for the model to learn action generalization. We support this claim with systematic empirical evidence, showing that even when conditioned on highly out of distribution (OOD) images, Diffusion Policy still outputs an action chunk from the training data. We evaluate and compare three representative policy families on the same data set: Diffusion Policy, Action Chunking with Transformers (ACT), and GR00T, a pre-trained generalist Vision-Language-Action (VLA) model. We show that Diffusion Policy gives strong action memorization giving surprising robustness in OOD regimes, ACT shows action interpolation with poor robustness in OOD regimes, and GR00T (benefiting from substantial pre-training) shows both action interpolation and OOD robustness. As a simple alternative to Diffusion Policy, we introduce the Action Lookup Table (ALT) policy, showing that an explicit lookup table policy can perform comparably in this low data regime. Despite its simplicity, ALT attains Diffusion Policy–level performance while also providing faster inference and explicit OOD detection via latent-distance thresholds. These results reframe diffusion policies for robot manipulation as reactive memory retrieval under data sparsity, and provide practical tools for interpreting, evaluating, and monitoring such policies. More information can be found at: \url{https://stanfordmsl.github.io/alt/}.

Reinforcement Learning · Multi-agent

Wei-Jer Chang, Akshay Rangesh, Kevin Joseph, Matthew Strong, Masayoshi Tomizuka, yihan hu, Wei Zhan

Developing autonomous vehicles (AVs) requires not only safety and efficiency, but also realistic, human-like behaviors that are socially aware and predictable. Achieving this requires sim agent policies that are human-like, fast, and scalable in multi-agent settings. Recent progress in imitation learning with large diffusion-based or tokenized models has shown that behaviors can be captured directly from human driving data, producing realistic policies. However, these models are computationally expensive, slow during inference, and struggle to adapt in reactive, closed-loop scenarios. In contrast, self-play reinforcement learning (RL) scales efficiently and naturally captures multi-agent interactions, but it often relies on heuristics and reward shaping, and the resulting policies can diverge from human norms. We propose human-like self-play, a framework that leverages a pretrained tokenized autoregressive motion model as a centralized reference policy to guide decentralized self-play. The reference model provides likelihood rewards and KL divergence, anchoring policies to the human driving distribution while preserving RL scalability. Evaluated on the Waymo Sim Agents Challenge, our method achieves competitive performance with imitation-learned policies while being up to 10× faster at inference and 50× smaller in parameter size than large generative models. In addition, we demonstrate in closed-loop ego planning evaluation tasks that our sim agents can effectively measure planner quality with fast and scalable traffic simulation, establishing a new paradigm for testing autonomous driving policies.

Fernando Ruiz-Mazo, Vikas Garg

Deploying ML systems with only a few real samples makes operational metrics (such as alert rates or mean scores) highly unstable. Existing uncertainty quantification (UQ) methods fail here: frequentist intervals ignore the deployed predictive rule, Bayesian posteriors assume continual refitting, and conformal methods offer per-example rather than long-run guarantees. We introduce a forecast-first UQ framework that blends the empirical distribution with a frozen pretrained generator using a unique Dirichlet schedule, ensuring time-consistent forecasts. Uncertainty is quantified via martingale posteriors: a lightweight, likelihood-free resampling method that simulates future forecasts under the deployed rule, yielding sharp, well-calibrated intervals for both current and long-run metrics without retraining or density evaluation. A single hyperparameter, set by a small-$n$ minimax criterion, balances sampling variance and model--data mismatch; for bounded scores, we provide finite-time drift guarantees. We also show how this framework informs optimal retraining decisions. Applicable off-the-shelf to frozen generators (flows, diffusion, autoregressive models, GANs) and linear metrics (means, tails, NLL), it outperforms bootstrap baselines across vision and language benchmarks (WikiText-2, CIFAR-10, and SVHN datasets); e.g., it achieves $\sim$90\% coverage on GPT-2 with 20 samples vs.\ 37\% for bootstrap. Importantly, our uncertainty estimates are operational under the deployed forecasting rule agnostic of the population parameters, affording practicable estimators for deployment in real world settings. Code available at \url{https://github.com/Aalto-QuML/Prequential/}.

Deep Learning · Generative Models and Autoencoders

Peter Blohm, Vikas Garg

Composing pretrained diffusion models provides a cost-effective mechanism to encode constraints and unlock complex generative capabilities. Prior work relies on crafting compositional operators that seek to extend set-theoretic notions such as union and intersection to diffusion models, e.g., using a product or mixture of the underlying energy functions. We expose the inadequacy and inconsistency of combining these operators in terms of limited mode coverage, biased sampling, instability under negation queries, and failure to satisfy basic compositional laws such as idempotency and distributivity. We introduce a principled calculus grounded in fuzzy logic that resolves these issues. Specifically, we define a general class of conjunction, disjunction, and negation operators that generalize the classical mixtures, illustrating how they circumvent various pathologies and enable precise combinatorial reasoning with score models. Beyond existing methods, the proposed *Dombi* operators yield complex generative outcomes, such as the Exclusive-OR (XOR) of individual scores. We establish rigorous theoretical guarantees on the stability and temperature scaling of Dombi compositions, and derive Feynman-Kac correctors to mitigate the sampling bias in score composition. Empirical results on image generation with stable diffusion and multi-objective molecular generation substantiate the conceptual, theoretical, and methodological benefits. Overall, this work lays the foundation for systematic design, analysis, and deployment of diffusion ensembles. Code is available at [https://github.com/Aalto-QuML/logic-diffusion-composition](https://github.com/Aalto-QuML/logic-diffusion-composition)

Deep Learning · Generative Models and Autoencoders

Hao Huang, Jingtao Ding, Mengqi Liao, Xin Wang, Jinyang Ban, Yuan Yuan, Huaiyu Wan, Yong Li

The widespread adoption of Low-Rank Adaptation (LoRA) for efficient fine-tuning of large language models has created demand for scalable parameter generation methods that can synthesize adaptation weights directly from task descriptions, avoiding costly task-specific training. We present LoRAGen, a structure-aware method for generating LoRA parameters from natural language descriptions. Through empirical analysis of LoRA libraries, we identify two key structural properties of LoRA parameter spaces: non-uniqueness of low-rank decomposition and heterogeneous weight distributions across network modules. These properties necessitate specialized parameter generation methods rather than general weight space learning approaches. LoRAGen employs a latent diffusion model with two innovations: weight-space supervision on full adaptation matrices to handle decomposition non-uniqueness, and a module-aware Mix-of-Experts decoder that adapts to module-specific weight distributions. Experiments show LoRAGen achieves 96.0\% performance relative to task-specific LoRAs on FLAN-T5-large and 72.7\% on Gemma-2-2B-Instruct for in-distribution tasks, while obtaining 40.2\% on zero-shot generation across unseen tasks—surpassing baselines by nearly 5\%. Our work establishes the first structure-aware approach to LoRA generation with insights into adaptation weight space geometry.

Computer Vision · Image and Video Generation

Gihoon Kim, Hyungjin Park, Taesup Kim

Personalizing text-to-image diffusion models involves integrating novel visual concepts from a small set of reference images while retaining the model’s original generative capabilities. However, this process often leads to overfitting, where the model ignores the user’s prompt and merely replicates the reference images. We attribute this issue to a fundamental misalignment between the true goals of personalization, which are subject fidelity and text alignment, and the training objectives of existing methods that fail to enforce both objectives simultaneously. Specifically, prior approaches often overlook the need to explicitly preserve the pretrained model’s output distribution, resulting in distributional drift that undermines diversity and coherence. To resolve these challenges, we introduce a Lipschitz-based regularization objective that constrains parameter updates during personalization, ensuring bounded deviation from the original distribution. This promotes consistency with the pretrained model’s behavior while enabling accurate adaptation to new concepts. Furthermore, our method offers a computationally efficient alternative to commonly used, resource-intensive sampling techniques. Through extensive experiments across diverse diffusion model architectures, we demonstrate that our approach achieves superior performance in both quantitative metrics and qualitative evaluations, consistently excelling in visual fidelity and prompt adherence. We further support these findings with comprehensive analyses, including ablation studies and visualizations.

Computer Vision · Image and Video Generation

Minjung Shin, Hyunin Cho, Sooyeon Go, Jin-Hwa Kim, Youngjung Uh

Multi-view generation with camera pose control and prompt-based customization are both essential elements for achieving controllable generative models. However, existing multi-view generation models do not support customization with geometric consistency, whereas customization models lack explicit viewpoint control, making them challenging to unify. Motivated by these gaps, we introduce a novel task, multi-view customization, which aims to jointly achieve multi-view camera pose control and customization. Due to the scarcity of training data in customization, existing multi-view generation models, which inherently rely on large-scale datasets, struggle to generalize to diverse prompts. To address this, we propose MVCustom, a novel diffusion-based framework explicitly designed to achieve both multi-view consistency and customization fidelity. In the training stage, MVCustom learns the subject's identity and geometry using a feature-field representation, incorporating the text-to-video diffusion backbone enhanced with dense spatio-temporal attention, which leverages temporal coherence for multi-view consistency. In the inference stage, we introduce two novel techniques: depth-aware feature rendering explicitly enforces geometric consistency, and consistent-aware latent completion ensures accurate perspective alignment of the customized subject and surrounding backgrounds. Extensive experiments demonstrate that MVCustom achieves the most balanced and consistent competitive performance across multi-view consistency, customization fidelity, demonstrating effective solution of multi-objective generation task.

Social Aspects · Trustworthy Machine Learning

Miso Kim, Georu Lee, Yunji Kim, Hoki Kim, Jinseong Park, Woojin Lee

Unlearning has emerged as a key technique to mitigate harmful content generation in diffusion models. However, existing methods often remove not only the target concept, but also benign co-occurring concepts. Unlearning nudity can unintentionally suppress the concept of person, preventing a model from generating images with person. We define these undesirably suppressed co-occurring concepts that must be preserved $\textbf{CARE}$ ($\textbf{C}$o-occurring $\textbf{A}$ssociated $\textbf{RE}$tained concepts). Then, we introduce the $\textbf{CARE score}$, a general metric that directly quantifies their preservation across unlearning tasks. With this foundation, we propose $\textbf{ReCARE}$ ($\textbf{R}$obust $\textbf{e}$rasure for $\textbf{CARE}$), a framework that explicitly safeguards CARE while erasing only the target concept. ReCARE automatically constructs the CARE-set, a curated vocabulary of benign co-occurring tokens extracted from target images, and leverages this vocabulary during training for stable unlearning. Extensive experiments across various target concepts ($\textit{Nudity}$, $\textit{Van Gogh}$ style, and $\textit{Tench}$ object) demonstrate that ReCARE achieves overall state-of-the-art performance in balancing robust concept erasure, overall utility, and CARE preservation.

General Machine Learning · Causality

Valentyn Melnychuk, Stefan Feuerriegel

Various deep generative models have been proposed to estimate potential outcomes distributions from observational data. However, none of them have the favorable theoretical property of general Neyman-orthogonality and, associated with it, quasi-oracle efficiency and double robustness. In this paper, we introduce a general suite of generative Neyman-orthogonal (doubly-robust) learners that estimate the conditional distributions of potential outcomes. Our proposed generative doubly-robust learners (GDR-learners) are flexible and can be instantiated with many state-of-the-art deep generative models. In particular, we develop GDR-learners based on (a) conditional normalizing flows (which we call GDR-CNFs), (b) conditional generative adversarial networks (GDR-CGANs), (c) conditional variational autoencoders (GDR-CVAEs), and (d) conditional diffusion models (GDR-CDMs). Unlike the existing methods, our GDR-learners possess the properties of quasi-oracle efficiency and rate double robustness, and are thus asymptotically optimal. In a series of (semi-)synthetic experiments, we demonstrate that our GDR-learners are very effective and outperform the existing methods in estimating the conditional distributions of potential outcomes.

Yunpeng Bai, Haoxiang Li, Qixing Huang

Diffusion Transformers (DiTs) have emerged as the dominant architecture for visual generation, powering state-of-the-art image and video models. By representing images as patch tokens with positional encodings (PEs), DiTs combine Transformer scalability with spatial and temporal inductive biases. In this work, we revisit how DiTs organize visual content and discover that patch tokens exhibit a surprising degree of independence: even when PEs are perturbed, DiTs still produce globally coherent outputs, indicating that spatial coherence is primarily governed by PEs. Motivated by this finding, we introduce the Positional Encoding Field (PE-Field), which extends positional encodings from the 2D plane to a structured 3D field. PE-Field incorporates depth-aware encodings for volumetric reasoning and hierarchical encodings for fine-grained sub-patch control, enabling DiTs to model geometry directly in 3D space. Our PE-Field–augmented DiT achieves state-of-the-art performance on single-image novel view synthesis and generalizes to controllable spatial image editing.

Applications · Language, Speech and Dialog

Zemin Huang, Yuhang Wang, Zhiyang Chen, Guo-Jun Qi

Mask-based Diffusion Language Models (DLMs) struggle to revise incorrect tokens: once a token is generated, it typically remains fixed. The key challenge is to identify potential errors in the inputs. In this paper, we propose Remasking-enabled Diffusion Language Model (RemeDi), a mask-based DLM that introduces remasking as another fundamental mechanism, enabling more flexible text refinement in diffusion-based text generation. To achieve this, RemeDi jointly predicts token distributions and per-token confidence scores at each step. The confidence scores determine which tokens to be unmasked after the current step, allowing the model to identify tokens with low quality and remask them. These remasked tokens can be resampled with richer context in subsequent steps. We design a remask-aware pipeline to train this ability, including supervised fine-tuning which teaches the model to detect and remask incorrect tokens in addition to predict mask tokens, and reinforcement learning which optimizes full generation trajectories toward higher rewards. Experiments show that RemeDi achieves the state-of-the-art results among open-source DLMs on multiple datasets.

Applications · Robotics

Yang Zhang, Chenwei Wang, ouyang lu, Yuan Zhao, Yunfei Ge, Zhenglong Sun, Xiu Li, Chi Zhang, Chenjia Bai, Xuelong Li

Vision-Language-Action (VLA) models pre-trained on large, diverse datasets show remarkable potential for general-purpose robotic manipulation. However, a primary bottleneck remains in adapting these models to downstream tasks, especially when the robot's embodiment or the task itself differs from the pre-training data. This discrepancy leads to a significant mismatch in action distributions, demanding extensive data and compute for effective fine-tuning. To address this challenge, we introduce Align-Then-stEer (ATE), a novel, data-efficient, and plug-and-play adaptation framework. ATE first aligns disparate action spaces by constructing a unified latent space, where a variational autoencoder constrained by reverse KL divergence embeds adaptation actions into modes of the pre-training action latent distribution. Subsequently, it steers the diffusion- or flow-based VLA's generation process during fine-tuning via a guidance mechanism that pushes the model's output distribution towards the target domain. We conduct extensive experiments on cross-embodiment and cross-task manipulation in both simulation and real world. Compared to direct fine-tuning of representative VLAs, our method improves the average multi-task success rate by up to 9.8% in simulation and achieves a striking 32% success rate gain in a real-world cross-embodiment setting. Our work presents a general and lightweight solution that greatly enhances the practicality of deploying VLA models to new robotic platforms and tasks. Our code is released at \url{https://github.com/TeleHuman/Align-Then-Steer}.

Zihao WANG, Yuzhou Chen, Shaogang Ren

Cross-modal image translation remains brittle and inefficient. Standard diffusion approaches often rely on a single, global linear transfer between domains. We find that this shortcut forces the sampler to traverse off-manifold, high-cost regions, inflating the correction burden and inviting semantic drift. We refer to this shared failure mode as fixed-schedule domain transfer. In this paper, we embed domain-shift dynamics directly into the generative process. Our model predicts a spatially varying mixing field at every reverse step and injects an explicit, target-consistent restoration term into the drift. This in-step guidance keeps large updates on-manifold and shifts the model’s role from global alignment to local residual correction. We provide a continuous-time formulation with an exact solution form and derive a practical first-order sampler that preserves marginal consistency. Empirically, across translation tasks in medical imaging, remote sensing, and electroluminescence semantic mapping, our framework improves structural fidelity and semantic consistency while converging in fewer denoising steps. The source code is in https://github.com/LaplaceLab/CDTSDE.

Optimization · Sampling and Optimization

Niels Mündler, Jasper Dekoninck, Martin Vechev

Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a formal language. Yet, due to their probabilistic nature, LLM output is not guaranteed to adhere to such formal languages. To address this, prior work has proposed constrained decoding to restrict LLM generation to particular formal languages. However, existing works are not applicable to the emerging paradigm of diffusion LLMs, as this requires supporting token generation in arbitrary order instead of the traditional left-to-right order. In this paper, we address this challenge and present the first constrained decoding method for diffusion models, one that can handle formal languages captured by context-free grammars. We begin by reducing constrained decoding to the more general additive infilling problem, which asks whether a partial output with holes can be completed to a valid word in the target language. This problem also naturally subsumes the previously unaddressed multi-region infilling constrained decoding. We then reduce this problem to the task of deciding whether the intersection of the target language and a regular language is empty and present an efficient algorithm to solve this task for context-free languages. Empirical results on various applications, such as C++ code infilling and structured data extraction in JSON, demonstrate that our method achieves near-perfect syntactic correctness while consistently preserving or improving functional correctness. Importantly, our efficiency optimizations ensure that the computational overhead remains practical.

General Machine Learning · Probabilistic Methods

Jonas Arruda, Vikas Pandey, Catherine Sherry, Margarida Barroso, Xavier Intes, Jan Hasenauer, Stefan Radev

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.

Computer Vision · Everything Else

Xiaoyang Liu, Zhengyan Zhou, Zihang Xu, Jiezhang Cao, Zheng Chen, Yulun Zhang

Recent advancements in image motion deblurring, driven by CNNs and transformers, have made significant progress. Large-scale pre-trained diffusion models, which are rich in real-world modeling, have shown great promise for high-quality image restoration tasks such as deblurring, demonstrating stronger generative capabilities than CNN and transformer-based methods. However, challenges such as unbearable inference time and compromised fidelity still limit the full potential of the diffusion models. To address this, we introduce FideDiff, a novel single-step diffusion model designed for high-fidelity deblurring. We reformulate motion deblurring as a diffusion-like process where each timestep represents a progressively blurred image, and we train a consistency model that aligns all timesteps to the same clean image. By reconstructing training data with matched blur trajectories, the model learns temporal consistency, enabling accurate one-step deblurring. We further enhance model performance by integrating Kernel ControlNet for blur kernel estimation and introducing adaptive timestep prediction. Our model achieves superior performance on full-reference metrics, surpassing previous diffusion-based methods and matching the performance of other state-of-the-art models. FideDiff offers a new direction for applying pre-trained diffusion models to high-fidelity image restoration tasks, establishing a robust baseline for further advancing diffusion models in real-world industrial applications. Our dataset and code will be available at https://github.com/xyLiu339/FideDiff.

Deep Learning · Generative Models and Autoencoders

Yunhong Min, Juil Koo, Seungwoo Yoo, Minhyuk Sung

We introduce BézierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. BézierFlow achieves a 2–3× performance improvement for sampling with $\leq$ 10 NFEs while requiring only 15 minutes of training. Recent lightweight training approaches have shown promise by learning optimal timesteps, but their scope remains restricted to ODE discretizations. To broaden this scope, we propose learning the optimal transformation of the sampling trajectory by parameterizing stochastic interpolant (SI) schedulers. The main challenge lies in designing a parameterization that satisfies critical desiderata, including boundary conditions, differentiability, and monotonicity of the SNR. To effectively meet these requirements, we represent scheduler functions as Bézier functions, where control points naturally enforce these properties. This reduces the problem to learning an ordered set of points in the time range, while the interpretation of the points changes from ODE timesteps to Bézier control points. Across a range of pretrained diffusion and flow models, BézierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to Bézier-based trajectory transformations.