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🚨Coming to #ICML2026 🇰🇷 Last year, we introduced Block Diffusion LMs, adopted by dLLMs at Google, NVIDIA, Meta, etc. 🚀Today, we introduce Set Diffusion, a faster, more flexible alternative that combines AR and diffusion by interpolating generation orders. 🧵1/8
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🧱Block Diffusion runs diffusion in fixed blocks, limiting any-order decoding and delaying KV-cache updates until block completion. 🤝 Set Diffusion runs diffusion in flexible token sets, enabling any-order decoding and KV-cache updates after every step. 2/8

⚖️Set Diffusion interpolates between full diffusion and AR by tuning: (1) set size for speed (2) generation order for quality-flexibility trade-offs. It recovers AR, full diffusion (e.g., MDLM/LLaDA), and Block Diffusion as special cases. 3/8

We induce generation order via position-dependent priority schedules, avoiding direct parameterization over combinatorial orderings. We introduce SW-DLMs: Set Diffusion LMs with sliding-window decoding, an order-causal transformer architecture, and low-variance training. 4/8

⏩Efficient Training. We denoise all sets in 1 forward pass with a set-causal transformer, where each set conditions on itself and previous clean sets. For training, singleton sets reduce this to a causal mask over the permuted sequence, with likelihoods for every context token. 5/8

💪Our Set Diffusion LMs improve key weaknesses of prior diffusion LMs: ✅ Better speed-quality tradeoffs on math, summarization, unconditional generation with stronger infilling than Block Diffusion. 6/8

✅ KV Caching: Set Diffusion caches KVs after each generated set. This is more efficient than Block Diffusion, which waits until block completion. ✅ Arbitrary-Length Generation: Sequential set modeling enables flexible-length generation, unlike full-sequence diffusion that uses fixed bidirectional context. 7/8

Catch me at poster #303 Thurs. morning! 🇰🇷📍 🧑🎓I’m a final-year Cornell CS PhD on the job market! Please reach out if you’re hiring in AI research. This work was done @cornell_tech with @volokuleshov 📄 🌐 🧑💻 🤗

very cool

thank you😁

Nice

available paper?

Very cool work! @mariannearr Wondering if this helps in quality as well? Sometimes smaller blocks are better. Or are the benefits tied mostly to caching ?

Thank you! Yes, similar to block diffusion, set diffusion also has a knob to tighten the likelihood bound for better quality. Smaller blocks in block diffusion make the NELBO tighter, but set diffusion exposes a different knob: the distribution over generation orderings. We increase the left-to-right generation bias by introducing position-dependent ordering schedules, which provably tighten the NELBO while better supporting flexible-position decoding. Empirically, this improves the speed–quality tradeoff relative to block diffusion. (more in Section 4

Does this work with phrased reasoning iteratively

KV-cache every step is the real unlock. Block partitioning was a workaround.
