# The Best ICML Papers of 2026, Simply Explained #113 Aug 3 Papers https://www.aibutsimple.com/p/the-best-icml-papers-of-2026-simply-explained 2025 was the year diffusion models moved out of image generation and into language and the year RL from verifiable rewards became the default way to finish training an LLM. We see this trend seep into 2026, especially at ICML. [ICML 2026](https://icml.cc/?utm_source=newsletter.aibutsimple.com&utm_medium=referral&utm_campaign=the-best-icml-papers-of-2026-simply-explained) recently ran from July 6-11, receiving 23,918 reviewed submissions and accepting 6,352 papers. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/aa9fa1b1-3cfe-43bb-941c-1d1d2b2239dd/ICML_2026_Papers__15_.png) Today, we’ll walk through 4 key papers: the two Outstanding Papers, plus 2 honorable mentions that have attracted large research attention. --- ### Papers Covered 1. The Flexibility Trap (Random Generation Order Makes DLMs Reason Worse) 2. High-accuracy sampling for diffusion models 3. How much can language models memorize? 4. And more… ### What's Helpful to Know - Diffusion language model (DLM/dLLM) - An LLM that uses diffusion for generation rather than an autoregressive approach. - They can either iteratively refine tokens or embeddings, generating portions of the full response at each denoising step. - Pass@k - Sample k answers; a problem is passed if any answer is correct. As k grows, Pass@k measures how much of the solution space a model can reach. - RLVR - Reinforcement learning from verifiable rewards, where the reward comes from an automatic check, such as running unit tests. - Density (p(x)) - The density p(x) is the probability density function (PDF) over the input data distribution. Higher values are assigned to samples more likely under the data. --- ### Random Generation Order Makes DLMs Reason Worse Paper: [The Flexibility Trap: Rethinking the Value of Arbitrary Order in Diffusion Language Models](https://arxiv.org/abs/2601.15165?utm_source=newsletter.aibutsimple.com&utm_medium=referral&utm_campaign=the-best-icml-papers-of-2026-simply-explained) Ni, Wang, Yue, et al., Tsinghua University and Alibaba, Outstanding ICML 2026 Paper A normal LLM generates tokens autoregressively, meaning left to right, one token per forward pass. A diffusion language model can take one of two approaches: diffuse on tokens (unmasking over time) or diffuse on embeddings (a continuous diffusion, then round to the nearest token). ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/14989454-fa7c-4af9-ad9f-074194414a77/ICML_2026_Papers__1_.png) A diffusive approach has 2 main benefits. First, it can fill several positions per step, so a 2,000-token answer might take 64 steps instead of 2,000 (speed). Second, generating these tokens in a random order (what we call any-order generation) seems expressive on paper, since there are many different ways to fill in a sequence of text. - It even contains the left-to-right (or autoregressive) as a special case, so it seems like it should do better. Random order generation is useful during inference, but the paper shows more options don’t exactly mean better reasoning during RL fine-tuning. This sequence below is more likely what unfolds: 1. At each denoising step, the model scores every masked position at once based on confidence. 2. A sampler decides which token positions to unmask. Typically, we unmask where the model is certain and leave uncertain positions masked. 3. Reasoning trajectories contain forking tokens, which are connectives like "therefore" and "since," which have high entropy. The words chosen as logical forks become important decision points, steering the rest of generation. 4. High entropy corresponds with low confidence, so forking tokens are deferred by the sampler until the end of generation. 5. By the time it returns to fill one in, text on both sides is committed. The authors call this entropy degradation. Averaged over all tokens, entropy is the same in both left-to-right and any-order, but if you look only at logical forks, arbitrary-order decoding becomes much more confident too early. The flexibility is being spent locking in easy tokens, and exploration pays for it. At Pass@1024 on HumanEval, left-to-right solves 21.3% of problems that arbitrary order misses, while arbitrary order only solves 0.6% of problems left-to-right misses. Arbitrary order explores a smaller space nested inside the other one. Given this finding, the authors adopt left-to-right diffusive generation during training, observing the past and masking the future: ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/cfd0ecce-e1fe-4d33-b0d6-a04a6d32b590/image.png) Here x~t is the input at step t, with tokens up to t−1 filled in and everything after masked. Additionally, they drop the order flexibility that existing RL methods diffusion LLMs use, under one fixed left-to-right trajectory, rather than approximating the marginalized probability from all possible trajectories (intractable). ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/5832aa07-d10b-41f6-af85-aa3295568d82/ICML_2026_Papers__3_.png) At inference time, the constraint is lifted, and the model will decode in parallel to maintain generation speed. Their method, JustGRPO (named after the RL algorithm GRPO), beats the best diffusion-specific RL methods by 3.0 on GSM8K and 6.1 points on Math500. --- ### Sampling Diffusion Models in Exponentially Fewer Steps Paper: [High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions](https://arxiv.org/abs/2602.01338?utm_source=newsletter.aibutsimple.com&utm_medium=referral&utm_campaign=the-best-icml-papers-of-2026-simply-explained) Chen, Chewi, Daskalakis, and Rakhlin, Outstanding ICML 2026 Paper Most diffusion models generate outputs the same (basic) way. We start from pure noise and iteratively step toward a data distribution, running a reverse noising process. In a score-based approach, at each step, the network computes what we call the score, which is the direction that the input should move to become more like data drawn from the target distribution. - Score-based methods and noise prediction methods (e.g., [DDPM](https://arxiv.org/abs/2006.11239?utm_source=newsletter.aibutsimple.com&utm_medium=referral&utm_campaign=the-best-icml-papers-of-2026-simply-explained)) are reparameterizations of each other, but we’ll discuss score here as it is more relevant to this paper. The score is the gradient of the log-density, represented as ∇xlog(p(x)). We’ll need this for later. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/7aec7357-2307-4b8c-a2e4-062b4aa2990c/ICML_2026_Papers__4_.png) But how many steps does this iterative approach take? The answer: quite a lot. In diffusion, the reverse process is a stochastic differential equation (SDE), and simulating it means splitting continuous time into discrete steps. That chopping shifts the distribution you actually sample from. Each step introduces a small approximation error, so the resulting distribution is not exactly the target distribution. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/67272091-fb2c-42ab-b341-a477dd604fb6/ICML_2026_Papers__5_.png) So, to reach an error of δ, the number of steps required scales by a polynomial of 1/δ. Demanding higher accuracy needs a rapidly (polynomially) increasing amount of compute. What’s surprising is that optimization and other methods are able to scale faster in ideal scenarios. Gradient descent can approach its optimum to an error of δ in only a polynomial-logarithmic scaling of 1/δ steps. Classical methods like markov chain monte-carlo (MCMC) achieve a similar property for sampling by using a correction (known as Metropolis-Hastings) after proposing a step. - It accepts or rejects it in a way that reduces the discretization error. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/83d0b7f5-bfe7-43ac-b713-743846e86d35/ICML_2026_Papers__6_.png) The issue is precisely since most diffusion models require the score (rather than the log-density, log(p(x))) that we cannot perform this correction. This paper shows how to perform the same type of correction using the score instead. The key observation is that we can integrate the score along a path to estimate the log-density ratio between two points. Seems simple, right? But we can’t integrate the score numerically, as we would need to discretize the integral as well. Instead, they use a randomized unbiased estimator of the integral. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/881c1889-07d9-4d01-bad5-7247b9d1e140/ICML_2026_Papers__8_.png) They also pair this with additional tricks, such as taking advantage of the Poisson distribution and using a Bernoulli factory. Overall, their method, called first-order rejection sampling, is able to simulate the accept-or-reject decisions, featuring polynomial-logarithmic scaling and the ability to work with the score directly. --- ### How Many Bits Can Language Models Memorize? Paper: [How much can language models memorize?](https://arxiv.org/abs/2505.24832?utm_source=newsletter.aibutsimple.com&utm_medium=referral&utm_campaign=the-best-icml-papers-of-2026-simply-explained) Morris, Sitawarin, Kokhlikyan, et al., FAIR at Meta, Google DeepMind, Cornell, NVIDIA, Outstanding ICML 2026 Paper Honorable Mention "Does this model memorize its training data?" is a legal, privacy, and scientific question all at once. In current literature, there are two standard ways of measuring this memorization: extraction and membership inference. Extraction asks whether you can prompt a model into reproducing a training example. - The issue with this is that models can be pushed into emitting almost anything. - For instance, a model that understands arithmetic can output 2 to the 30th power as 1073741824 without ever having seen the number. Membership inference asks whether a particular sample was in the training data. - Here, information is defined at the level of the whole dataset, so membership inference can’t tell you how much of one specific source resides in the parameters. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/39e414a5-c988-4d5c-ae17-11ffa102949e/ICML_2026_Papers__9_.png) Both methods blend memorization with competence, while this paper uses a definition borrowed from information theory. Let X be the dataset, theta-hat be the trained model, and θ be the true process that generated the data. The authors then define total memorization as the mutual information between the dataset and the model (θ-hat). ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/1f2e4bdf-03be-4b2b-ae83-2a8741afc00d/image.png) Then, unintended memorization is defined as what survives after you also condition on the generation process θ: ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/873841fa-b47f-4615-b00c-53996c4635f1/image.png) Above, H is entropy, so the first term is the uncertainty left in the dataset once you know how it was generated, and the second is the uncertainty left once you know that plus the trained model. The gap between them is what the model has unintentionally memorized. - This is the additional information about the dataset beyond what’s explained by the data generation process. Essentially, we hold fixed everything you could predict from knowing how the data was made, then count the bits the model still supplies additionally. We can subtract the unintended memorization from the total memorization to obtain the intended memorization, or generalization. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/bc049d0e-30de-4006-947e-365c0455e567/image.png) The authors trained a model on uniformly random bitstrings as an experiment. Random data has no structure to generalize about, so total memorization equals unintended memorization exactly. They tried datasets of increasing sizes and saw that the amount of memorized bits climbed, then flattened out. The plateau is the model's capacity. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/58ceb023-d65e-41cc-ac91-33923bd95a33/ICML_2026_Papers__11_.png) They divided this capacity by the parameter count (of the GPT family, 500K-1.5B) and obtained an approximate 3.6 bits-per-parameter. Going from bfloat16 to float32 moves that number only from 3.51 to 3.83. Doubling the precision buys little change, telling us that the capacity is not stored in the [mantissa](https://newsletter.aibutsimple.com/p/quantization-for-llms-simply-explained). Their key conclusion is that models will memorize until their capacities fill, then start to “grok,” when unintended memorization decreases as they start to generalize. ![](https://media.beehiiv.com/cdn-cgi/image/fit=scale-down,width=1200,format=auto,onerror=redirect,quality=80/uploads/asset/file/b3044e85-3c21-41e0-ba96-a8786bc635fb/image.png) Official figure from the paper --- ### Conclusion Letting a diffusion LLM pick its own token order does not help it reason, because it defers the forking tokens (high-entropy connectives) that significantly affect neighboring tokens. You can now sample a diffusion model to a low error without as many steps by rejection sampling an integral estimate of the score. Researchers can now measure memorization in bits. It comes to roughly 3.6 per parameter, and crossing that ceiling with your dataset is where double descent starts. And the flexibility trap returns in the closing pair, since it's the one with a consequence attached. The open question worth watching is whether a smarter sampler fixes the flexibility trap or whether any-order generation is stuck with it. To read our breakdown of the other papers we’ve covered in this post, upgrade to PRO to get more visual insights and deeper dives. We’ll dive into how a paper detects lies inside RLVR rewards, how 2 diffusion models magically generate the same images given different training data, and more.