Classifier-free guidance cost and bias

Use ε_u for the null-conditioned prediction and ε_c for the conditional prediction, evaluated at the same latent and noise coordinate. The common pipeline convention adds w times their difference to ε_u. Here w=1 gives the conditional prediction and w=0 the null prediction; w greater than one extrapolates beyond the conditional value. The original classifier-free guidance paper expresses its coefficient relative to the conditional baseline, so its named weight can differ by one. Record the actual formula rather than comparing naked guidance numbers across implementations.

A negative prompt can replace the null branch with another condition, which is not literally the unconditional data distribution. Noise prediction, score prediction, and clean-data prediction must be combined and converted consistently with the algorithm. Diffusers v0.35.1’s classic StableDiffusionPipeline demonstrates the ε_u+w(ε_c−ε_u) convention in its pinned implementation. These endpoint identities describe the formula. Without timestep-guidance embeddings, the classic pipeline enables two-branch CFG only for guidance_scale greater than one; at values at most one it normally follows its conditional-only path, so passing zero is not an unconditional request. Other model families can use distilled guidance embeddings or different conditioning mechanisms; their cost and scale semantics should not be inferred from this two-branch example.

Two logical branches per image per evaluation can be run sequentially or concatenated into a larger batch. Concatenation can reduce launch overhead and improve utilization, but one call over twice the batch still performs both branches and needs their intermediate storage. Actual latency is not necessarily exactly doubled because kernels, occupancy, memory pressure, and overhead vary with batch. Measure the implementation at the intended resolution and precision rather than counting host calls as though they were fixed-cost units.

Guidance can be enabled for only part of a trajectory or changed by callbacks, but that changes the executed sampler policy and can affect a multistep history. Record the schedule of guidance values and corresponding branch batch shapes. A comparison that reduces guidance work while also changing adherence or diversity is a tradeoff, not a pure implementation speedup. Include conditioning encoders, scheduler work, latent decoding, and queueing when translating denoiser branch counts into request latency.

With exact conditional and unconditional scores at a fixed noise level, their linear combination is the gradient of a corresponding weighted log-density expression when that expression is normalizable. That instantaneous identity does not prove the guided family is the marginals of the same forward diffusion or that a finite reverse solver exactly samples a simple terminal tempered law. Learned score fields add further approximation. Measure adherence, diversity, saturation, artifacts, and coverage under the guidance policy instead of presenting increased scale as a universally unbiased improvement.

The vector instrument illustrates linear magnitude amplification only. Reset, set both angle=0° and magnitude=1, predict x-component one and y-component zero, then Play or Step. Separately Reset, set both angle=0° and magnitude=3, predict x-component three and y-component zero, then Play or Step. These supported controls show a threefold component scale without predicting whether that direction is desirable. The lab does not contain conditional denoisers, their difference field, guidance batching, or image quality. Stronger field magnitude alone is not evidence of better generated samples.