How does selective looping in diffusion models differ from recurrence in autoregressive architectures?

This reads the question as: when a diffusion model selectively loops some of its layers, is that a different *kind* of repeated computation than the recurrence you find in looped or recurrent transformers built on the autoregressive side? The corpus suggests the two share a mechanism but split on what the looping is *for*. Both are bets that reusing computation beats adding fresh parameters. LoopMDM shows selective layer looping in a masked diffusion model matching same-size models at 3.3× fewer FLOPs and beating deeper non-looped baselines on reasoning Does looping layers beat adding depth in diffusion models?, while on the transformer side looped models converge each cycle to a fixed point and essentially re-enact the same feedforward inference stages rather than computing anything new How do looped transformer layers actually behave during inference?. So at the level of 'reuse layers to get effective depth,' they rhyme.

The deeper difference is what the repetition iterates *over*. Recurrence in autoregressive-style architectures iterates along a sequence or a reasoning trajectory — one token, one step, one timescale after another. The Hierarchical Reasoning Model makes this explicit, coupling slow planning and fast computation across two timescales to escape the fixed-depth ceiling that constrains a plain transformer Can recurrent hierarchies achieve reasoning that transformers cannot?. Diffusion's looping, by contrast, sits inside a *parallel* denoising process: the whole sequence is refined simultaneously, with continuous latent variables letting gradients flow across every position at once — the very thing that lets Diffusion-LM hit global control targets autoregressive methods can't reach Can diffusion models enable control that autoregressive models cannot reach?. Selective looping in that setting deepens a non-sequential refinement, not a left-to-right unroll.

That distinction has teeth. Because diffusion generates non-sequentially, it breaks the log-likelihood factorization that recurrent/autoregressive training leans on — which is exactly why reinforcement learning methods transfer so badly to diffusion models and need trajectory marginalization or outcome-based workarounds Why can't we easily adapt reinforcement learning to diffusion language models?. The looping is the same idea; the substrate it loops over is incompatible enough that downstream training machinery doesn't carry across.

Worth knowing: the choice between sequential recurrence and parallel diffusion may be more contingent than it looks. LLaDA shows non-autoregressive diffusion matching autoregressive scaling, arguing scalability comes from transformers, data, and Fisher consistency rather than from sequential factorization itself Does autoregressive generation uniquely enable LLM scaling?. And hybrids are eroding the line entirely — block-wise autoregressive diffusion reclaims AR's KV-cache efficiency while keeping diffusion's parallel decoding Can diffusion language models match autoregressive inference speed?. The interesting frontier isn't 'which loop wins' but where each one's repetition does work the other structurally can't reach — autoregressive recurrence still can't retract an emitted token the way constraint solving needs Why does autoregressive generation fail at constraint satisfaction?, a limit diffusion's iterative re-masking sidesteps by construction.