Models & learning
Flow matching
Flow matching is a generative-model training method that learns a time-dependent vector field transporting samples from a simple prior distribution to a data distribution. Training regresses the vector field along chosen probability paths without solving the flow during each update; generation starts from the prior and numerically integrates the learned ordinary differential equation.
Also known as: FM, flow-matching objective
Updated
Learning a vector field
Flow Matching for Generative Modeling defines probability paths between a tractable prior and a target data distribution. A neural network receives a point on a path and its time, then predicts the velocity that should move the point along that path.
For a straight conditional path between a noise sample and a data sample, the target velocity is their difference. Training is ordinary regression: sample both endpoints and a time, interpolate a point, and minimise the error between predicted and target velocity.
Generating a sample
Inference begins with a sample from the prior, commonly a standard Gaussian. An ordinary differential equation solver repeatedly applies the learned vector field from the prior endpoint to the data endpoint. Euler integration is the simplest numerical rule, although other solvers and schedules can trade compute for accuracy.
The path direction, target-velocity sign and integration direction must agree. Reversing one without the others moves samples towards noise rather than towards the learned data distribution.
Relationship to diffusion and robot actions
Diffusion models can be expressed through particular probability paths and vector fields. Flow matching also permits straighter transport-style paths, which may need fewer integration steps than a stochastic diffusion sampler. It is a broader training framework, not a synonym for diffusion.
π0 and SmolVLA apply conditional flow matching to continuous robot action chunks. Images, language and robot state condition the vector field, while integration transforms an initial noisy chunk into executable action values.
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Related terms
Models & learning
Diffusion policy
A diffusion policy is a learned robot policy that generates an action or action sequence through iterative denoising conditioned on observations and, where applicable, a task goal. This formulation can represent several plausible behaviours for the same scene and is commonly trained by imitation on time-aligned trajectories of observations and expert actions.
Models & learning
Action chunking
Action chunking is a policy design in which one observation is used to predict a sequence of several future robot actions rather than a single next action. The chunk can capture short-term motion structure and reduce the effective number of sequential predictions, while its execution and replanning schedule determine how quickly the robot can react to new observations.
Models & learning
Vision-language-action model
A vision-language-action model is a robot policy that conditions on visual observations and natural-language instructions to predict executable actions. It adapts a pretrained vision-language model, or a similar multimodal backbone, using robot trajectories so that semantic knowledge is connected to an embodiment’s action space. The action representation may use discrete tokens or continuous values.
Models & learning
Robot foundation model
A robot foundation model is a broadly pretrained model intended to provide a reusable starting point for multiple robot tasks, environments or embodiments. It learns from diverse robotics and sometimes web or human data, then acts directly or is adapted with target-domain data. The term describes a training and reuse strategy, not one fixed architecture.