Part 13 — Discussion: choosing a route to build¶

The route chapters deliberately picked no winner — they laid out trade-offs and kept the options live. This chapter does the opposite, on purpose: it answers the practitioner's question. Of all these, which do you build first, and why? The answer is a reasoned recommendation, not a law — and it depends on what you are trying to do.

Recap — where this sits. Parts 6–10 surveyed the routes neutrally; Parts 11–12 assembled specific choices into two applications. This chapter steps back and makes a recommendation — which is a different kind of document, so read it that way: an opinion argued from the trade-offs, explicit about the goal it assumes and honest about the fork where a different goal would flip it. Nothing new mechanically; everything here was built earlier.

A tutorial can responsibly present every route as a legitimate option. A builder cannot build all of them — and shouldn't. You implement one well, plus maybe a baseline or two for benchmarking, and you want that one to be both the most promising and the cheapest to stand up. Those two criteria normally pull in opposite directions. The interesting claim of this chapter is that, for one very common goal, they collapse onto a single choice — and seeing why is more useful than the answer itself.

1. First, clear the field — Route D is phase two¶

Route D is out of contention as a first build, and not because it is weak. It produces decisions — the intervention \(p^{*}\) that minimizes the planning energy \(\mathcal{E}(p) = \lVert g_\phi(z_b, e(p)) - z_{\text{goal}} \rVert^2\) — not data. It closes neither gap, and it presupposes a forward generator to plan over. You cannot build the planning layer before the thing it plans on exists. So Route D is a phase-two capability by construction: it wraps a calibrated forward model once you have one. That leaves Routes A, B, C, and the conditional flow prior (Part 9) as the genuine contenders for "turn JEPA into an effective generative model."

2. The lens that decides it¶

Your two criteria usually trade off, and the table makes the tension visible:

Route	"Most promising" (effectiveness)	"First to develop" (cost / proximity to existing code)
A (Gaussian head)	Low — unimodal per condition; risks being a CVAE in a JEPA hat	Highest — an afternoon's wiring
B (Gaussian variational)	Medium — principled, but the same Gaussian floor	Medium — adds a prior network + KL balancing
C (conditioned diffusion)	Highest — fully expressive, modular	Lowest — a second model, many-step sampling
Part 9 (conditional flow prior)	High — expressive and modular like C	High — one extra input to code you already run

Read the two columns and the usual dilemma is stark: A is cheapest but ineffective on exactly the responses that matter; C is most effective but heaviest. With no existing code you would face a real choice — prototype with A and accept the Gaussian floor, or pay for C up front. What dissolves the dilemma is the word effective in the question, together with what is already sitting in the repo.

3. The recommendation — the conditional flow prior + a count decoder¶

For the goal of "predict the calibrated distribution of responses to an intervention," build the conditional flow prior as the G1 mechanism, married to Route A's count decoder for G2. In the four-route vocabulary, that is a Route B core realized at its flow limit rather than with a Gaussian — which, as Part 9 showed, is simultaneously Route C done with rectified flow. You are not dodging the A/B/C question; you are picking the single object where B and C coincide, and bolting Route A's decoder on the end.

Three reasons it wins as a first build, each from an earlier chapter:

It skips the Gaussian floor for free. A Gaussian head (A or B) is unimodal per condition, and the canonical failure — the two-fates problem — is routine in the domains this series targets: a perturbation drives identical cells to fate X or fate Y, so the true response is genuinely bimodal, and a single Gaussian confidently predicts the empty valley between them. You would build the Gaussian version, watch it fail on the benchmark, and climb the expressive-posterior ladder anyway. The flow prior is the top of that ladder — multimodal and correlated from the start.
It is modular like Route C, without diffusion's weight. Freeze the encoder, train the flow on frozen latents; no reconstruction gradient touches the encoder, so the "did JEPA quietly become a reconstruction model?" collapse risk (A/B's central hazard) is structurally absent. But rectified flow's near-straight paths sample in a handful of integration steps where a diffusion denoiser wants many.
It is the gentlest expressive generator to train — one velocity-MSE, no adversary, no noise schedule, no KL weight to balance — and you have already debugged its unconditional twin (the Parts 0–4 starter), so the training dynamics are known territory, not new risk.

The one-line case. "Most promising" and "first to develop" normally trade off; here they collapse onto the conditional flow prior, because for this codebase the expressive option costs about the same as the Gaussian floor you would otherwise build and discard.

4. But sequence it honestly — the build order¶

The route is the conditional flow prior; the order you build it in should respect two disciplines the route chapters were right to insist on.

Build G2 — the count decoder — first. The load-bearing piece for the benchmark is not the fancy prior; it is the decoder that reaches data space, because that is where effect size lives (the NB head of Part 6: a softmax gene-rate \(\rho\), dispersion \(\kappa\), mean assembled as \(\mu = \ell \cdot \rho\), trained on the count likelihood). Every route shares it; you need it regardless.
Keep Route A's Gaussian head as the baseline you are obligated to beat. This is the experiment the whole arc hangs on: a from-scratch conditional NB-VAE. If your JEPA-pretrained conditional-flow model does not beat it on effect size, calibration, and data efficiency, the JEPA pretraining and the flow expressiveness bought nothing — and you want to know that early. The Gaussian head is cheap, closed-form, and one-shot: an ideal debugging and baselining instrument even though it is not the final answer.

So the order is: (1) NB/ZINB decoder + Gaussian-head baseline → (2) swap the Gaussian head for the conditional flow field \(v_\eta(z, t, c)\) → (3) escalate to full conditioned diffusion only if flow's expressiveness proves insufficient on your data → (4) wrap Route D planning around the calibrated forward model for screening.

flowchart LR
    D["(1) count decoder<br/>+ Gaussian-head baseline"] --> F["(2) swap in conditional<br/>flow prior v_η(z,t,c)"]
    F -->|"only if flow underfits"| C["(3) full conditioned diffusion"]
    F --> P["(4) wrap Route D planning<br/>(screening)"]
    classDef accent fill:#eef2ff,stroke:#6366f1,color:#1e1b4b;
    classDef io fill:#f8fafc,stroke:#94a3b8,color:#0f172a;
    class F accent;
    class D,C,P io;

5. Route A vs Route B — the distinction worth holding¶

These two come up as "similar but different," and the cleanest way to keep them straight is a single test. They can be the same picture architecturally — predictor emits Gaussian parameters, you sample, you decode — so the wiring is not the tell. The tell is the objective.

The one-question litmus. During training, is there a network that gets to see the true outcome and produce a distribution from it?

Yes → Route B. That network is the posterior \(q_\phi(z \mid z_b, z_p)\) — it is allowed to peek at the answer during training. A learnable conditional prior \(\pi(z \mid z_b, z_p)\) — which cannot peek, and is what you sample from at generation — is pulled toward it by a \(\mathrm{KL}(q_\phi \Vert \pi)\) term. This is amortized variational inference: a CVAE built on purpose.

No → Route A. The stochasticity is just a noise input, shaped by whatever reconstruction pressure happened to produce. A CVAE you fell into.

The consequence is what makes the distinction matter: Route B's spread is trained to match reality (calibrated by construction); Route A's spread is calibrated by luck. That calibration is the entire reason to pay Route B's KL-balancing tax. And here is the punchline that ties A → B → Part 9 together: the conditional flow prior reaches Route B's expressive ceiling without paying Route B's KL tax — pure flow-matching, no posterior/prior pair, yet a distribution of the same (in fact richer) expressive class. That is not bookkeeping; it is the practical reason the flow is the right thing to build.

(One honest note on the equivalence: "B and C coincide at Part 9" is a statement about the object — the class of conditional distributions you can represent — not about the training recipe. Route B's recipe and the bare flow-matching recipe are different objectives that converge to the same expressive class.)

6. Where the novelty lives — two parallel angles, both open¶

A caution that the verdict above can obscure, and the most important strategic point in this chapter: the flow is the substrate, not the contribution. A conditional flow-matching prior over a frozen latent plus a count decoder is architecturally close to existing latent-generative models, and (as Part 9 notes) flow-versus-diffusion is nearly cosmetic in capability. So "build the conditional flow prior" answers which vehicle, not what is new. If the aim is genuinely beyond state-of-the-art, the novelty must come from elsewhere — and there are two candidate sources, kept here as parallel, open directions rather than a settled pick:

Structured conditioning (the action-operator angle). If the conditioning is not a generic embedding but operator-structured — named, composable generators in the \(\exp(M)\) form of the Operator World Models line (an active, still-developing companion line in this project) — the model gains capabilities generic latent-generative models lack: predicting unseen combinations by composing intervention operators, interpreting what an intervention does to the latent (its generator's spectrum), and an explain-away-safe surprise signal. This is where reliable, useful, and novel converge, and the conditional flow becomes the expressive sampler riding on top of a structured world model.
The JEPA-pretraining payoff (the empirical angle). A rigorous result that JEPA pretraining + a calibrated generative head recovers the effect-size signal that latent-only JEPA misses (recall Cell-JEPA found JEPA improves representation but not effect-size estimation) and beats reconstruction-based generative models on it. That is a testable, benchmark-driven contribution in its own right.

Neither is settled; both are worth pursuing. The point for this chapter is only to keep them in view, so that building the conditional flow prior is understood as standing up the vehicle for a contribution that lives in the conditioning structure or the demonstrated representation payoff — not mistaken for the contribution itself.

7. The fork that would flip the recommendation¶

Every recommendation has a hidden assumption, and honesty means naming it. This one assumes the goal is "predict the calibrated distribution of responses to an intervention." For that, the conditional flow prior plus count decoder is the strongest first method and the one you are closest to shipping.

But the flow gives an implicit density — you sample by integrating, with a likelihood available only through the ODE change-of-variables, and broken in data space by any decoder placed after it (Part 5 §5). So if the near-term goal is de-novo design or variant-style scoring (\(\log p(\text{ref})\) vs \(\log p(\text{alt})\)) — capabilities this lab's genomics ambitions point toward — the calculus changes: you would want to keep the generative process in a single space where the probability-flow ODE stays exact, or reach for a different family altogether. That open likelihood problem is the one none of the routes close.

The recommendation, stated with its assumption. If the goal is calibrated response-distribution prediction (the perturbation and chronic-disease applications of this series), build the conditional flow prior + count decoder, decoder first, with the Gaussian head as the baseline to beat. If de-novo design or likelihood scoring is a near-term requirement, treat that as a different problem and reconsider the family. Keep both forks live until the goal is fixed.

8. Where this leaves the builder¶

Build first: the count decoder (G2, effect size), then the conditional flow prior \(v_\eta(z, t, c)\) as the G1 mechanism — Route B's expressive limit and Route C-with-flow at once, cheapest on existing code.
Always benchmark against: a from-scratch conditional NB-VAE; if JEPA + flow doesn't beat it, find out early.
Hold the novelty elsewhere: in the structured conditioning (operator-informed) and/or the demonstrated JEPA-effect-size payoff — the flow is the substrate.
Respect the fork: the recommendation is for response-distribution prediction; de-novo design / scoring changes it.

That is the practitioner's path through a design space the rest of the series was careful not to collapse — collapsed here, deliberately, with the seams left visible.

Previous: Part 12 — Application: digital phenotyping. The route deep-dives: Part 6 (A), Part 7 (B), Part 8 (C), Part 9 (conditional flow prior), Part 10 (D). Back to the series overview.