Latest / Embodied AI 101 / Stop Starting From Noise: Action-to-Action Flow Matching for Fast Robot Control
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- Stop Starting From Noise: Action-to-Action Flow Matching for Fast Robot Control. Action-to-Action Flow Matching • Jindou Jia, Gen Li, Xiangyu Chen, Tuo An, Yuxuan Hu, Jingliang Li, Xinying Guo, and Jianfei Yang • MARS Lab, Nanyang Technological University • Robotics: Science and Systems 2026 / arXiv • 2026. The Big Idea. Here is the shortest way to understand Action-to-Action Flow Matching, or A2A: it does not primarily invent a better denoiser. It changes where action generation begins. A conventional diffusion or flow-matching policy asks: starting from random noise, and conditioned on what the robot currently sees, how do we iteratively transform that noise into a valid action chunk?. A2A asks a more robotics-specific question: given what the robot has just executed, how should that recent motion be transformed into the next action chunk?. That shift sounds almost obvious in retrospect. Robots do not wake up from statistical amnesia at every control cycle. They have encoders, joint sensors, controller feedback, and a recent trajectory through configuration space. On most manipulation tasks, the next several commands are strongly related to the last several executed states. A2A treats that history not merely as another conditioning variable, but as the actual source distribution of the generative process. The policy learns a flow from past motion to future motion, rather than from Gaussian noise to future motion. That is the paper’s most durable contribution. It elevates the source distribution from a fixed modeling convention to an explicit robot-policy design choice. Before going further, there are two bibliographic clarifications. The supplied July 30 publication date does not appear to be the paper’s primary publication date. The first arXiv version was submitted on February 7, 2026, the current second version was posted on May 7, and the work was subsequently presented at RSS 2026, whose main conference ran from July 13 through July 17 in Sydney. The full author list also contains eight researchers, with Jindou Jia and Gen Li marked as equal contributors and Jianfei Yang as corresponding author. The second clarification concerns scope. A2A is not, by itself, a language-conditioned generalist robot model, nor does the paper demonstrate repurposing a pretrained generalist policy. Its experiments train task-level visuomotor imitation policies on five simulated and two real-world manipulation tasks. Its relevance to generalist policies is architectural: A2A could potentially replace the Gaussian-source action head inside a larger VLA or multitask policy, but that integration is not evaluated here. Why Noise-to-Action Became the Default. Diffusion Policy helped establish action diffusion as one of the strongest templates for visuomotor imitation learning. Instead of regressing directly to one action, it learns a field that repeatedly refines a noisy action trajectory. Combined with action chunking, visual conditioning, and receding-horizon execution, this formulation handles high-dimensional continuous outputs and can commit to one of several valid behaviors rather than averaging incompatible demonstrations. But the Gaussian source in diffusion policies came largely from generative modeling traditions outside robotics. If a model must synthesize an image without an existing image trajectory to continue, an isotropic noise distribution is a sensible universal starting point. It makes few assumptions and can, in principle, cover the entire target distribution. For a robot in closed-loop operation, that source is much less natural. The robot already knows roughly where it is, how it has been moving, and what its low-level controller actually achieved. Beginning each action chunk from independent noise deliberately discards that information and then asks a network to recover it through conditioning. The practical consequence is iterative computation. Traditional DDPM-style policies may evaluate a relatively expensive U-Net or transformer tens or hundreds of times per action prediction. Flow matching shortens and straightens the generative path, but typical flow policies still integrate an ordinary differential equation from noise to actions over multiple network evaluations. On a static benchmark, that is an efficiency issue. In a real control loop, it is also a freshness issue: observations continue to age while the policy is generating the action intended to respond to them. A2A’s argument is that robotics provides a free warm start. Adjacent action chunks are not independent samples from an arbitrary distribution. They arise from the same physical trajectory. Joint positions cannot teleport, end-effector poses usually change smoothly, and actuator limits impose substantial local structure. If the source is already near the target, perhaps a small MLP and one Euler step are enough. The important distinction is that A2A does not simply concatenate the previous action with image features. That would still leave the generative state initialized from noise. Instead, the encoded history becomes the point transported by the flow. Vision tells the flow where that motion should go next, but proprioceptive history supplies the object being moved. A Data-Dependent Flow. Standard conditional flow matching begins with a source sample, usually Gaussian noise, and a target data sample. During training, it chooses a random point along the straight line connecting them. The network is asked to predict the velocity that would carry the interpolated point along that path. At inference, the learned velocity field is integrated from source time zero to target time one. A2A keeps this machinery but replaces the source sample. For every training example, the method takes a history of executed proprioceptive states or actions and pairs it with the future action chunk from the same trajectory. In the paper’s default configuration, both the historical and future horizons contain eight steps. The history is encoded into a source latent, while the future action chunk is encoded into a target latent. A vision encoder processes the recent camera observations and supplies a global condition to the flow network. The use of executed history matters. The authors explicitly recommend deriving the source sequence from proprioceptive feedback rather than recycling the commands that the policy previously issued. A commanded position and an achieved position can differ because of tracking error, contact, saturation, delay, or low-level controller dynamics. Flowing from old commands would make the high-level policy operate inside its own imagined trajectory. Flowing from measured execution closes that loop. The action semantics are task-dependent. The paper uses joint angles in simulation and end-effector states in its real-robot experiments. This choice is more consequential than it first appears. A2A works most naturally when historical feedback and predicted controls occupy compatible coordinate systems. If a system predicts absolute joint targets, measured joint positions provide a meaningful source. If it predicts joint velocities, torques, or pose deltas, raw positions may no longer be a locally aligned source without an appropriate transformation. A2A therefore expresses a broader pattern rather than one universal tensor interface:. Find a physically meaningful representation of recent execution that lives close to the representation of the next command, and use it as the generative source. That source could be joint positions, end-effector trajectories, spline coefficients, latent motor primitives, or some hybrid state-action history. The paper demonstrates two of those possibilities, not all of them. Inside the Architecture. The network has three paths: vision, historical motion, and future actions. The vision path uses a ResNet-18 followed by a linear projection. Recent observations are encoded and combined into a 512-dimensional global conditioning vector. The released configuration uses random cropping, group normalization, ImageNet-style input normalization, and a ResNet initialized without pretrained weights. The historical path applies a temporal one-dimensional convolutional encoder to the previous eight proprioceptive states. The released encoder uses three convolutional layers with kernel size five and stride two, followed by a linear projection into the same 512-dimensional space. A corresponding encoder maps the target future action chunk into another 512-dimensional vector. The open-source implementation uses separate history and future encoders with the same general structure, rather than forcing both chunks through a single shared encoder. That implementation detail is worth noticing. The paper motivates A2A by saying that past and future chunks are naturally close because of physical continuity. But the learned encoders are also free to reshape their respective distributions until they become easier to transport. In other words, the short path is partly supplied by physics and partly manufactured by representation learning. This is not a flaw. It may be exactly why the method works. A raw eight-step joint trajectory does not necessarily have Euclidean geometry that is ideal for flow matching. Expanding it into 512 dimensions gives the network space to separate motion phases, encode derivatives implicitly, and align semantically similar transitions. Still, it means the claim should be phrased carefully: A2A learns a latent geometry in which historical and future chunks can be transported efficiently; it does not prove that they were already close under the raw action metric. The flow network itself is lightweight. The paper describes adaptive-layer-normalized MLP blocks, while the released default configuration uses a four-layer flow network with 512 hidden dimensions, an MLP expansion ratio of four, and no dropout. Six integration steps are the default, even though the paper also evaluates four-step and one-step operation. Finally, an MLP decoder maps the transported target latent back to the future action sequence. Because most computation after image encoding happens in a fixed-width latent vector rather than over an action-time feature map, the action generator is substantially lighter than a temporal U-Net or action transformer. Three Losses Hold the Latent Space Together. The flow-matching objective alone is not the entire method. A2A uses three coupled losses. The first is the standard flow loss. At a randomly sampled flow time, the model sees an interpolation between the history latent and the future-action latent. It predicts the displacement field that should carry the former into the latter. The second is an action-autoencoder reconstruction loss. The future-action encoder and decoder must preserve enough information to reconstruct the original action chunk. Without this constraint, the latent space could become easy to transport through but useless for control. The third is an inference-consistency loss. During training, A2A actually integrates the predicted flow from the history latent, decodes the resulting endpoint, and compares both the endpoint latent and reconstructed actions with the ground truth. This directly supervises the trajectory that will be used at deployment, rather than relying only on velocity matching at randomly sampled intermediate times. This third term is especially important for interpreting the results. A2A is not merely benefiting from a better initialization. It is also trained to make its finite-step numerical solver land correctly. The released implementation computes a latent consistency loss and an L1 reconstruction loss on the flow-generated actions, with nonzero weights for both target reconstruction and flow reconstruction. It also complicates the phrase “training efficiency.” The paper demonstrates rapid convergence in epochs and demonstrations, which is valuable. But inference consistency performs flow sampling inside the training loop, so fewer epochs do not automatically imply fewer GPU-hours than every baseline. The paper does not present a comprehensive wall-clock or total-FLOP comparison of training. The safest conclusion is that A2A is optimization- and data-efficient under the reported training schedule, not necessarily that every training step is cheaper. Single-step inference provides another useful interpretation. With one Euler step, the network effectively takes the encoded history and predicts one large conditioned residual that should land at the future-action latent. That begins to resemble a learned residual dynamics model or regression policy. The distinction from regression becomes meaningful through the random flow-time supervision, the latent path structure, the possibility of taking multiple integration steps, and—when noise is introduced—the ability to sample different futures. What the Experiments Actually Show. The simulation evaluation covers Close Box from RLBench, Pick Cube and Stack Cube from ManiSkill, and Open Drawer and Pick-Place Bowl from LIBERO, all exposed through RoboVerse. Real-world experiments use a Franka robot on Pick Cube and Open Drawer. The comparison includes DDPM, DDIM, score-based, and flow-matching policies with U-Net or DiT backbones, as well as ACT and VITA. Horizons, batch size, and model scale are standardized where possible. Under the paper’s intentionally short training regime of 100 demonstrations and 30 epochs, A2A obtains success rates of 92, 92, 86, 92, and 90 percent across the five simulation tasks. That is roughly a 90 percent average. VITA is the closest competitor and wins Pick-Place Bowl, but A2A leads on the other four tasks. The largest gaps appear on Stack Cube and Open Drawer, where several noise-based diffusion and flow baselines have not yet converged. The key phrase is “not yet converged.” Additional experiments show that the DDPM-UNet and FM-UNet baselines can eventually approach 100 percent with more epochs. A2A’s strongest training claim is therefore rapid convergence, not an unbeatable asymptotic performance ceiling. On Close Box, it reaches a stable 100 percent success rate within about 40 epochs. On Stack Cube, it reaches and maintains a high ceiling as demonstration count increases, while the baseline curves fluctuate more. The inference-step experiment is more distinctive. Performance improves quickly over the first few integration steps and largely saturates after four. When limited to one step, success surpasses 90 percent after roughly 32 training epochs on Close Box. The authors visualize history and future latents with t-SNE and report that paired distances shrink while flow directions become increasingly parallel during training. That visualization is suggestive, but it should not be treated as formal proof that the high-dimensional flow is straight. t-SNE intentionally distorts global geometry, and the encoders themselves are changing during training. More convincing future analysis would report latent-space transport costs, vector-field curvature, numerical integration error, and endpoint error directly in the original 512-dimensional space. Nevertheless, the task success results establish the practical point: a single learned update can often be sufficient. The reported one-step latency is 0.56 milliseconds on an NVIDIA RTX 5090, with multi-step A2A remaining below roughly one millisecond per reported inference measurement. That is a striking model-side number, but it is not a complete sensor-to-actuator latency. It should not be interpreted as including camera exposure, image transfer, preprocessing, robot middleware, network communication, safety checks, and low-level controller delay. It also comes from a high-end desktop GPU rather than a typical embedded deployment computer. Even with those caveats, reducing the action generator from dozens of large-network calls to one small latent MLP evaluation is meaningful. It frees compute for larger visual encoders, higher control rates, uncertainty estimation, or asynchronous replanning. Real-Robot Data Efficiency and Visual Robustness. In the real-world Pick Cube experiment, policies are trained from 30 trajectories and evaluated over ten trials. A2A reaches 100 percent in-distribution success. The Open Drawer experiment likewise uses 30 trajectories and finds that A2A completes the task more directly, while DDPM-UNet and FM-UNet show visible hesitation and longer completion times. The authors also collect just ten demonstrations at each of two new cube locations and report rapid adaptation, including a difficult location near the edge of the camera’s field of view. The most memorable real-world result replaces the training cube with a previously unseen glowing object. The tested diffusion and flow baselines fail all ten attempts, while A2A succeeds in eight. The proposed explanation is that A2A does not require vision to reconstruct the entire local motion state on every query. Recent proprioception anchors the trajectory, leaving vision to specify how that trajectory should be corrected. That is plausible, but ten trials make this an illustrative stress test rather than a precise estimate of population-level robustness. The glowing object also changes appearance more dramatically than geometry or task structure. A broader evaluation would separately vary texture, shape, material, object identity, occlusion, and target ambiguity. The simulation domain-randomization results provide more coverage. All policies train on Level 0. A2A with six flow steps scores 100 percent on that level, then 38, 42, and 38 percent as novel backgrounds, lighting, and camera viewpoints are added. The one-step model scores 20, 16, and 22 percent on those out-of-distribution levels. Competing methods generally fall into the low single digits. So A2A is relatively much more robust, but the absolute result remains sobering. A success rate around 40 percent is not deployment-grade generalization. The paper demonstrates that proprioceptive anchoring reduces visual brittleness; it does not remove it. Determinism, Multimodality, and History Noise. The base A2A policy has a conceptual weakness: for a fixed observation and fixed action history, its source is deterministic. Unlike a Gaussian-start diffusion model, it has no independent latent variable from which to sample alternative futures. If demonstrations contain two equally valid continuations from the same state, base A2A tends to collapse onto one. The authors address this by perturbing historical actions with small Gaussian noise before encoding them. In a two-dimensional navigation example with valid paths on both sides of an obstacle, deterministic A2A selects one route, while noise with standard deviation 0.02 allows it to express both modes without losing task success. Noise also improves robustness to source uncertainty. A2A is more sensitive than noise-start baselines when the robot begins from an unseen configuration, which is unsurprising: an unusual history moves the source outside its familiar transport geometry. Adding history noise during training substantially improves initial-state generalization. In a visual-randomization experiment, a 0.02 perturbation raises Level 1 performance from 20 to 52 percent. For the initial-state experiment, the paper examines a larger 0.1 standard deviation. There is no single settled noise scale. The repository recommends 0.02 as a practical default, while the released A2A-Noise class defaults to 0.1. That class adds noise to normalized raw history before encoding, and its current prediction method also samples noise at inference—not only during training. Researchers adopting the code should therefore decide explicitly whether they want stochastic deployment, training-only augmentation, or a learned state-dependent source variance. This design tension points toward a deeper question: how much of the source should be trustworthy physical state, and how much should be stochastic capacity? Too little noise loses multimodality and may overfit to nominal trajectories. Too much noise destroys the warm start that makes A2A attractive. How A2A Fits Into the Fast-Policy Landscape. A2A is part of a broader movement away from long, unconditional noise-to-action trajectories. FlowPolicy retains a noise source but modifies the flow objective to enforce velocity consistency, allowing single-step action generation from point-cloud observations. Its main lever is the geometry of the learned vector field. A2A’s main lever is the location of the source. These strategies are potentially complementary: one could use a history-informed source together with consistency-flow training. VITA takes a more radical noise-free route. It treats visual latents themselves as the source of a flow into latent actions, eliminating a separate visual-conditioning pathway. Like A2A, it introduces an action autoencoder and endpoint decoding losses to stabilize the latent space. The difference is informational responsibility. VITA asks vision to provide both the source and task context; A2A grounds the source in proprioceptive history and reserves vision for conditioning. That likely contributes to A2A’s resilience under visual distraction, while creating greater dependence on reliable state history. Warm-Start Diffusion provides the generic generative-model version of the same intuition. It trains a deterministic model to predict a context-dependent Gaussian mean and variance, then begins diffusion from that informed distribution. A2A avoids an auxiliary source predictor by taking a physical sequence already available on the robot. A particularly close follow-up is LeaP, released after A2A in June 2026. LeaP learns a proprioception-conditioned diagonal Gaussian over action chunks, explicitly balancing informed initialization with stochasticity. Relative to A2A, it gives up the simplicity of using history directly but gains an adaptive variance and a source that can be attached to different downstream generators. Comparing direct history transport against a learned stochastic prior is now an important experimental question. Legato, another RSS 2026 work, approaches continuity from action-chunk execution. It trains flow-based VLA policies using mixtures of known actions and noise so that new chunks continue smoothly from partially committed actions, particularly under variable inference delay. A2A uses an encoded historical window as the source; Legato shapes the denoising schedule around known action prefixes. Both reject the idea that every chunk should be generated independently from scratch. There is also an interesting tension with Much Ado About Noising. That work argues that much of the benefit attributed to generative robot policies may actually come from supervised iterative computation and carefully chosen stochasticity, rather than accurate multimodal distribution fitting. A2A demonstrates strong one-step performance, which pushes against the need for long iterative compute. But it also relies on inference-consistency supervision, learned latent geometry, and optional stochastic perturbations. A clean comparison between one-step A2A and a capacity-matched residual regression model would help separate the value of flow supervision from the value of the source prior. The authors’ own regression ablation moves in that direction. Latent regression performs similarly in-distribution but degrades more severely under visual perturbation than latent flow matching. That is encouraging evidence for the generative objective, although the evaluation is too narrow to settle the larger regression-versus-generation debate. Finally, the same group’s subsequent FLASH policy extends the history-anchored idea from discrete action chunks to Legendre-polynomial trajectory coefficients. One inference can then describe a much longer continuous trajectory, and analytic differentiation supplies feed-forward velocity targets to the controller. FLASH suggests that A2A is best viewed not as a finished architecture, but as the first instance of a broader history-anchored trajectory-generation program. What I Would Change Before Deployment. For a lab considering A2A, the first task is not selecting the number of flow steps. It is defining the source semantics. Use measured execution in coordinates compatible with the output. If the policy predicts absolute joint positions, joint-position history is natural. For velocity, torque, or delta-pose policies, consider deriving historical controls in the same representation rather than feeding raw configuration. Treat hybrid action spaces explicitly. The authors acknowledge that binary gripper commands and other switch-like dimensions do not obey the same continuity assumptions. A separate categorical head, event detector, or contact-phase model is preferable to forcing every dimension through the same continuous flow. Stress-test resets and recovery states. The source prior is strongest during nominal continuation and weakest after emergency stops, controller saturation, human intervention, collisions, or episode initialization. Training should include corrupted histories, padded startup buffers, and trajectories recovering from off-manifold states. Tune stochasticity as a deployment variable. The useful choice is not merely “A2A or A2A-Noise.” Test training-only perturbations, inference-time sampling, state-dependent variance, and selective noise on ambiguous motion dimensions. The paper’s use of both 0.02 and 0.1 shows that the correct scale is task-dependent. Profile end-to-end latency on the target machine. A sub-millisecond flow head may still sit behind a large visual backbone. Measure camera-to-command delay, not just ODE integration, and compare one, two, four, and six steps under the same control frequency. Report both convergence and total training cost. Reproduce the epoch-efficiency curves, but also record wall-clock time, network evaluations, and energy use. Inference-consistency training may trade additional training computation for much cheaper deployment. The released code is integrated into RoboVerse, exposes base and noisy variants, supports the project’s simulation workflow, and is licensed under Apache 2.0. The authors recommend reproducing the simulation advantage and establishing a working Diffusion Policy baseline before attempting a real-robot port, largely because observation alignment, history buffering, and action normalization are easy to get subtly wrong. For integration into a generalist VLA, I would keep the large vision-language backbone unchanged and replace only the action expert. Language, image, and task tokens would condition the flow, while embodiment-specific proprioceptive adapters would map recent execution into a shared action latent. A mode or skill variable would probably be necessary so that continuity does not prevent intentional phase changes—for example, transitioning from approach to grasp, or abandoning a failed grasp and beginning recovery. That proposal is an extrapolation, not a result in the paper. A2A has yet to demonstrate cross-task pretraining, language grounding, cross-embodiment transfer, or adaptation of frozen generalist models. The Video Experiment—and What It Really Means. The paper also applies the idea to future-frame prediction under the name Frames-to-Frames Flow Matching. Three historical frames are encoded into a 512-dimensional source latent, a transformer flow network transports that latent, and a convolutional decoder predicts the next three frames. The experiment uses 100 videos from each of five Pick Cube randomization levels, trains for 500 epochs, and evaluates four unseen scenes. The model produces better future frames than a deterministic regression baseline with otherwise similar architecture. This supports the general principle that temporally adjacent distributions can provide informative generative sources. But it is a proof of concept, not evidence that A2A is ready to replace contemporary video diffusion models. The dataset, horizon, visual diversity, and model size are all small. The more interesting future direction would be to close the loop: predict a future visual latent from recent frames, use it to condition an A2A action flow, and test whether the additional world-model signal improves recovery or long-horizon planning. Final Assessment. A2A’s headline number is 0.56 milliseconds. Its more important contribution is conceptual. Robot-policy research has spent enormous effort improving how a model travels from noise to action: better samplers, straighter flows, consistency objectives, distillation, and larger action experts. A2A asks whether noise was the right departure point in the first place. For smooth manipulation under reliable proprioceptive feedback, the answer is often no. Recent execution is already a strong local prior. Encoding it as the source of a latent flow can simplify the transport problem enough that a small MLP and one integration step perform competitively with much heavier diffusion policies. The paper backs that claim with strong short-budget training results, credible real-robot demonstrations, and unusually large relative gains under visual perturbation. The limits are equally clear. Base A2A is deterministic, unusual initial states can corrupt its source, discrete events violate its continuity assumptions, and absolute out-of-distribution success remains modest. The experiments do not yet establish scaling to generalist VLAs or long-horizon, contact-rich tasks. The learned encoders and consistency loss also contribute substantially, making it difficult to attribute every gain solely to physical proximity between past and future actions. Even so, A2A opens a valuable design axis. When building the next generative robot policy, the first question should no longer be only, “Which diffusion or flow objective should we use?”. It should also be:. What does the robot already know that would make a better source than noise?.