PONDER: Learning to Generate in the Right Order

Generative modeling of discrete data has two popular paradigms: autoregressive models such as GPT, which factorize a sequence in a left-to-right (L2R) order, and masked diffusion models, which are essentially any-order autoregressive modeling. Rather than competing methods, these are the two extreme points of a single axis -- the generation order. For structured discrete domains without a natural traversal, both extremes may be suboptimal, yet the intermediate choice -- a single well-adapted order -- remains largely unexplored. We introduce OrderGPT, which builds on Any-Order GPT to learn a task-level generation order without canonical-order supervision. Our key observation is that predicting variables from randomly sampled reveal prefixes produces recurring attention patterns in the backbone that provide a model-dependent signal of predictive dependencies. We aggregate this signal into a reciprocal dependency graph and use a spectral teacher to derive continuous generation priorities. A lightweight OrderMLP integrated into the GPT backbone learns to predict these priorities from attention, incorporating order learning into the architecture within a single training run. Training gradually shifts toward the learned order, which is then frozen for subsequent autoregressive training and generation. The same mechanism adapts across modalities: adaptively it recovers near-L2R dependency structure in language, learns anatomically organized factorizations on human pose, and discovers a factorization on tabular data that places statistically and semantically related fields nearby, while improving downstream modeling metrics across all domains. The code is available at https://github.com/Chenhe-yang/OrderGPT/.

Autoregressive (AR) image generators are powerful in principle but inflexible in practice: training with a fixed raster-scan order hardcodes a single factorization of the image distribution into the model, leaving it unable to inpaint, outpaint, or edit at inference time. Existing solutions, including the modern discrete-diffusion family, train from scratch on a mixture of token orderings, paying roughly 3x the compute of standard raster-scan training; discrete diffusion further sacrifices compatibility with the AR inference ecosystem (KV caching, vLLM) by construction. We argue that this cost is unnecessary. A pretrained raster-scan AR model has already learned the joint distribution over image tokens; what it lacks is not knowledge but the ability to express that knowledge through non-sequential conditional pathways. We propose a recipe for adapting pretrained raster-scan models into any-order generators using two components: future-aware positional embeddings that resolve a target-position identifiability problem at negligible overhead, and an ordering curriculum that traces a stable optimization path from the pretrained solution to a good any-order basin. Applied to four base models across two architectures and two scales (LlamaGen-L/XL, RAR-L/XL), the recipe substantially outperforms MaskGIT on ImageNet inpainting (FID 6.21 vs. 10.44) and outpainting, is competitive with MAR-L, trades a 1.2-1.9 increase in class-conditional FID for this flexibility, and costs 13-33% additional compute beyond pretraining, while leaving the standard AR inference stack untouched. Inpainting, outpainting, and editing, our results suggest, need not be added to autoregressive image models. They can be unlocked from the ones that exist. Code is available at https://github.com/Ordered-AR/unlockedadaptation.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, CoFRe. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8%, training time by 11.5%, and VRAM by 16.9%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6% and VRAM by 50.7%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.