We compare diffusion-based and autoregressive language models under CheckList-style perturbations. We frame semantics-preserving perturbations as potentially containing an off-manifold component and hypothesise that diffusion denoising can reduce the resulting output change relative to autoregressive decoding. We evaluate eight instruction-tuned 7-9B models (three diffusion, five autoregressive) across sentiment, QQP, and SQuAD using behavioural pass rates and a perturbation coefficient that measures output change relative to input change. Results are task-dependent. Behaviourally, diffusion gains 18.2 and 11.0 points overall on QQP and SQuAD, while autoregressive models perform better on the sentiment and SQuAD invariance slices. On QQP, the all-model coefficient ratio does not favour diffusion ( ̂γ_AR/ ̂α_Diff ≈ 0.91); excluding two autoregressive models with strong label-prior effects as a diagnostic sensitivity analysis yields 1.23 overall and 1.48 on invariance tests. Diffusion also performs worse on perturbations that should change the output. Thus, the observed stability differences are task-conditional, and because the empirical diffusion coefficients exceed one, the experiments do not directly validate the contraction assumption of our theoretical proposition. Data and code are available at: https://github.com/AarushRathore1729/dlm_ar_final.

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and trainability. In recent years, multiple LRNN-based architectures have been proposed, each introducing distinct parameterizations, discretization schemes, and implementation constraints. However, existing implementations are fragmented across different software frameworks, often rely on framework-specific optimizations, and in some cases require custom CUDA kernels or lack publicly available code altogether. As a result, using, comparing, or extending LRNNs requires substantial implementation effort. To address this, we introduce lrnnx, a unified software library that implements several modern LRNN architectures under a common interface. The library exposes multiple levels of control, allowing users to work directly with core components or higher-level model abstractions. lrnnx aims to improve accessibility, reproducibility, and extensibility of LRNN research and applications. We make our code available under a permissive MIT license.