flow-based trajectory generation

Generative trajectory planning struggles with stitching multiple trajectory segments under out-of-distribution boundary conditions (e.g., zero-shot start-goal pairs) and complex obstacle avoidance. Method: We propose the first invertible flow-based framework explicitly designed for stable trajectory stitching. Our approach introduces a boundary-condition-guided sampling mechanism, a segment-alignment loss function, and explicit incorporation of kinematic constraints; it further employs a stitching-aware data construction strategy and a co-designed training-inference paradigm. Results: Evaluated on both Franka Panda simulation and real-robot platforms, our method achieves large-scale obstacle avoidance (obstacles up to 4× larger than baselines) and zero-shot cross-domain planning. It significantly outperforms existing generative planners and, for the first time, enables controllable, robust, multi-segment trajectory stitching—marking a critical advance in compositional motion planning.

Rectified Flow (RF) models exhibit fundamental theoretical and architectural differences from conventional diffusion models, rendering existing acceleration techniques incompatible. To address this, we propose the first end-to-end efficient acceleration framework specifically designed for RF. Our method introduces three core innovations: (1) batched velocity field modeling, which decouples temporal dependencies to enable parallel computation; (2) heterogeneous timestep vectorized scheduling, optimizing hardware utilization; and (3) dynamic TensorRT compilation, achieving operator-level optimization and memory-access co-design. By tightly integrating flow-matching theory with system-level optimizations, our framework achieves up to 611% speedup on 512×512 image generation—significantly surpassing the current average acceleration of 18% across general-purpose methods—and enables, for the first time, efficient high-resolution deployment of RF models.

This work investigates whether flow matching in temporal generation learns a universal dynamical structure or merely reproduces historical trajectories. By analyzing the empirical flow matching objective under Gaussian conditional paths, we derive—for the first time—a closed-form expression for its optimal velocity field, revealing it to be a similarity-weighted mixture of historical instantaneous velocities. This formulation constitutes a nonparametric, memory-augmented continuous-time dynamical system. Building on this insight, we propose a training-free closed-form sampler that directly generates high-quality probabilistic forecasts from historical transitions. Evaluated on nonlinear dynamical system benchmarks, our method substantially improves sampling efficiency and numerical stability while offering an explicit, interpretable mechanism for data-dependent dynamics.

Discrete-state-space generative models—e.g., for small molecules, DNA, and protein sequences—lack principled, controllable guidance mechanisms. Existing continuous-domain guidance paradigms do not generalize to discrete spaces, hindering attribute-controlled generation. Method: This paper introduces the first general, differentiable guidance framework for discrete generative models based on continuous-time Markov processes, unifying discrete diffusion and flow-matching architectures. It overcomes the fundamental incompatibility of continuous guidance with discrete state spaces by establishing a theoretically grounded guidance theory for discrete domains. The framework enables arbitrary differentiable guidance objectives without model retraining, leveraging probability path reweighting and gradient-driven discrete sampling. Contribution/Results: Experiments demonstrate substantial improvements in target property satisfaction rates and sample diversity across diverse biomolecular generation tasks, while maintaining flexibility and strong generalization across guidance objectives and model architectures.

This work addresses the issue of blurred and detail-deficient samples in unguided generation with pretrained flow models, which arises from the smoothing effect of neural networks. While existing guidance methods like classifier-free guidance (CFG) improve fidelity, they incur substantial computational overhead and compromise sample diversity. To overcome these limitations, we propose Momentum Guidance (MG), a plug-and-play technique that leverages historical velocity information along the ODE trajectory via exponential moving average to extrapolate the current velocity—introducing no additional computational cost. MG can be used independently or combined with CFG, achieving an average FID improvement of 36.68% without CFG and 25.52% with CFG on ImageNet-256 (reaching an FID of 1.597 with 64-step sampling). Furthermore, MG consistently enhances both generation quality and diversity across large-scale models such as Stable Diffusion 3 and FLUX.1-dev.

Path planning in complex environments requires simultaneous reasoning about spatial geometry and global structural constraints. This work proposes FlowPlanner, the first approach to integrate diffusion models and flow matching into path planning, enabling end-to-end generation of feasible trajectories directly from random noise under multi-channel conditioning—including obstacle maps and start-goal configurations. FlowPlanner demonstrates emergent reasoning capabilities, consistently producing constraint-satisfying paths with high success rates even with very few generation steps. The method significantly outperforms conventional CNN-based baselines, highlighting the promise of generative modeling for structured decision-making tasks.

This work addresses the challenge of achieving high-quality generation with drastically reduced inference steps, enabling efficient one-step or few-step synthesis. The authors propose a unified few-step generation framework based on cumulative flow matching, which introduces cumulative flow abstraction and cumulative parameterization to jointly model local instantaneous updates and global probability transport over finite time horizons. Notably, this approach requires no increase in model capacity or architectural modifications, making it readily applicable to a broad range of diffusion and flow-based models. Empirical evaluations across diverse tasks—including image generation, geometric distribution modeling, joint prediction, and signed distance field (SDF) synthesis—demonstrate that the framework achieves compelling generation quality at substantially lower inference costs, highlighting its strong versatility and computational efficiency.

This work addresses the inconsistency between training and inference constraints in robot motion generation by proposing ConFlow, a novel framework that integrates constraint guidance directly into flow matching. ConFlow explicitly models task constraints through differentiable obstacle or cost functions and replaces the standard Gaussian prior with a conditional Gaussian process to enforce trajectory smoothness and boundary conditions. Additionally, it leverages infeasible trajectories as negative supervision signals to enhance constraint adherence. Experimental results demonstrate that ConFlow significantly reduces collision rates and improves trajectory quality in dual-robot navigation tasks, outperforming existing flow matching approaches both with and without inference-time guidance.

Existing controllable generation methods often rely on fine-tuning, auxiliary networks, or test-time search, lacking a flexible, training-free control mechanism. This work proposes a “follow-the-mean” principle within the flow matching framework: by adjusting the conditional terminal mean and leveraging a reference set, it guides a pre-trained generative model to achieve desired attribute control. The approach employs deterministic interpolation-based flow matching, closed-form terminal mean correction, and semi-parametric guidance combining a frozen FLUX.2-klein model with a learnable residual refiner, enabling reference set swapping at inference time. Under fixed prompts, seeds, and weights, it effectively controls color, identity, style, and structure. Notably, this semi-parametric method attains unconditional DiT-B/4-level generation quality on AFHQv2.