Ask any active-inference modeler which time axis their generative model runs on, and you have quietly asked half the design question. The rest is which factors, which precisions, and which policies. This note is about the time axis: when a discrete-time Partially Observable Markov Decision Process (POMDP) is the honest frame, and when a continuous-time formulation earns the extra math it costs. Class E
The two shapes of a generative model
Parr, Pezzulo, and Friston (2022) work both formulations side by side because both are needed, not because either is optional. The discrete-time POMDP posits hidden states that change at ticks, categorical observations tied to those states by a likelihood matrix, and policies that choose among a small set of actions per tick. Free energy is a sum over ticks, expected free energy scores each policy at planning depth, and Bayesian inference over states and policies proceeds by matrix updates you can actually watch converge. Class E
The continuous-time formulation lives in stochastic differential equations. Hidden states drift under a flow, sensory channels emit continuously, and the agent minimizes variational free energy along generalized coordinates of motion (position, velocity, acceleration, and higher orders of the state). Action is not a categorical choice but a control signal on a reflex arc. The Markov blanket sits at the boundary between internal and external dynamics, and precision weights on prediction errors modulate how strongly each channel pulls on inference. Class E
When discrete-time is the right frame
Discrete-time POMDPs earn their place when the world is naturally chunked: decisions at pauses, moves in a maze, treatments across sessions, deployments across days. The Precision Lab, the Echo Lab, and the Loop Lab are all discrete-time by design, because the phenomena they steer are already discrete at the level a person can reason about them. Class C The Cell Lab discretizes a service cell that is itself a sequence of scheduling decisions, which is the right level for a pre-registered falsification benchmark on a hidden 216-state system. Class C
The engineering payoff is not small. Categorical likelihoods and transition matrices are inspectable. Policy enumeration is finite, so planning depth is a dial and expected free energy is a table you can print. KL divergence between prior preferences and posterior predictions has a closed form. When we want the lab to be a teaching instrument, discreteness is what makes the math steerable in a browser without a numerical stack. Class C
When continuous-time earns its keep
Continuous-time formulations are the honest frame for closed-loop physiology, motor control, and any system where the interesting behavior lives in the derivatives. The cardio-renal loop the Heart Lab models is one such case: baroreflex and volume regulation do not wait for ticks, and generalized coordinates of motion let the model track a trajectory rather than a snapshot. Class C Chemotaxis, saccade dynamics, and postural sway sit in the same neighborhood.
The cost is real. Continuous-time inference typically requires numerical integration, a choice of basis for generalized coordinates, and a precision structure over both sensory channels and their derivatives. Falsification is harder because more of the model's behavior is buried in solver choices and initial conditions. That is not a reason to avoid the formulation, it is a reason to earn it: use continuous-time when the phenomenon itself is continuous and the added structure buys you a claim you could not make in the discrete frame. Class E
What the choice is not
The choice is not between rigorous and approximate. Both formulations are rigorous inside their scope. The choice is not between neural and non-neural either: both can be implemented in neural machinery under the free energy principle, and both can be simulated without one. It is a modeler's choice about where the boundary between world and agent is drawn, and how the flow across that boundary is quantified.
The blessed working hypothesis for our program is that UNI is on an attainable path toward General Natural Intelligence, natural not artificial, a working hypothesis whose evidence is growing, evidence-classed, and tested in the open. Getting the time axis right is one of the first places that hypothesis has to earn its keep. If your generative model chunks the world at the wrong scale, no amount of precision tuning downstream will fix it.
A practical rule of thumb
Start discrete when the decision structure is discrete, the observations are categorical, and the agent must choose among a small set of policies at each step. Move to continuous when the derivatives carry the meaning, the sensory channel is a signal not a symbol, and control is a flow rather than a click. When you are unsure, write the discrete model first: it will tell you whether the phenomenon actually needs the continuous machinery. Class C