Realistic handwritten text generation plays an important role in numerous applications, such as font design, biometric authentication, and robotic calligraphy. Existing methods are typically divided into two independent paradigms: online approaches that estimate handwriting trajectories and offline approaches that synthesize realistic handwriting images. While online models capture structural and temporal dynamics, they often lack fine-grained textures, whereas offline models reproduce realistic appearance but discard stroke order. However, unifying online and offline models remains challenging due to (1) the lack of an explicit physical model linking stroke kinematics to pixel-level appearance and (2) the absence of paired trajectory-image datasets. Moreover, enabling end-to-end learning requires a differentiable rendering process across motion and appearance domains. To address these challenges, we propose a compact physical brush model that bridges stroke dynamics and visual appearance, together with a differentiable rendering module that converts stroke trajectories into stylized images. By integrating these components, we propose a unified online-offline handwriting generation framework via differentiable brush rendering. The proposed framework consists of four core modules: 1) a text-to-stroke generator that predicts the target stroke conditioned on the given text and style image, 2) a brush parameter observer that extracts brush model parameters from style references, 3) a differentiable brush renderer that maps a stroke sequence and physical brush parameters into a handwritten image, and 4) a zero-shot image refiner that refines rendered images via diffusion models. Extensive experiments and real-world robotic calligraphy demonstrations validate our approach, achieving both structural and visual fidelity.
Realistic online handwriting depends not only on individual character shapes, but also on how a writer connects, spaces, and aligns adjacent characters. Existing methods rely primarily on long-range sequence modeling and capture these inter-character behaviors only implicitly. This often produces plausible glyphs accompanied by broken cursive joins, inconsistent spacing, or writer-inconsistent transitions. We introduce BoundInk, a writer-conditioned framework that treats inter-character boundaries as explicit generation units. By jointly modeling local transitions and surrounding text context, BoundInk preserves writer-specific glyph appearance while improving connectivity and spacing across complete text lines. We further introduce a boundary-aware evaluation framework that directly assesses cursive continuity and spatial relationships between characters beyond conventional trajectory similarity. Across three benchmark-matched settings, BoundInk improves all applicable boundary-quality measures and reduces normalized dynamic time warping by 17.6--47.8%. In blind human evaluations, BoundInk outputs are preferred in 78.0--82.6% of valid criterion-wise judgments.
Recovering online pen trajectories from offline handwriting images, often referred to as handwriting trajectory recovery (stroke recovery), is an offline-to-online conversion task with applications in stroke-level editing and forensic analysis. We propose, to the best of our knowledge, the first diffusion-model-based framework for this task. Our method formulates trajectory recovery as image-conditioned generation and uses a denoising diffusion model to sample pen trajectories consistent with the observed ink trace. Through extensive quantitative evaluations on CASIA-OLHWDB (1.0-1.1), we verify that the proposed approach enables accurate recovery even for complex multi-stroke characters, substantially improving both temporal similarity (DTW/LDTW) and shape fidelity (AIoU) over representative prior methods such as PEN-Net and Cross-VAE. We further show that the model captures general stroke-order tendencies and generalizes to classes unseen during training, exemplified by cross-script transfer: a model trained on Chinese characters can recover reasonable stroke orders for Latin letters to some extent.
Teaching machines to emulate natural handwriting styles remains an open challenge, as it requires synthesizing stroke sequences that dynamically vary in shape, texture, pressure and script - not only across individuals, but also within a single person's handwriting. Attempts at this challenge have largely explored deep learning methods in both online and offline settings. However, these approaches are often constrained by style-specific architectural choices, heavy reliance on large datasets, high compute costs, and a lack of flexible control over writing styles through natural language. To this end, we introduce HandwritingAgent, a language-driven agent that can synthesize natural handwriting sequences directly in Scalable Vector Graphics (SVG) format with no need for style-specific training. The agent leverages a large reasoning model to geometrically analyse and autoregressively generate target handwritten glyphs as stroke sequences in a discrete grid canvas environment. Generation is conditioned on texts provided in either conversational or non-conversational mode, along with a reference handwriting-style image. Experiments on diverse handwriting tasks spanning imitation, recognition, multi-lingual handwriting synthesis, and generation of complex handwritten maths and science expressions indicate substantial improvement in performance, with HandwritingAgent matching or surpassing state-of-the-art generative handwriting models, while providing a more efficient, controllable, and generalizable synthesis method.