SGA: Plug&Play Geometric Verification for Educational Video Synthesis

Large language models can generate executable code for educational animations, but the resulting renders often exhibit visual defects, including element overlap, misalignment, and broken animation continuity. These defects cannot be reliably detected from the code alone and become apparent only after execution. We formalize this problem as render-feedback-aware constrained code generation: given a natural language specification, the model must generate executable code whose rendered output satisfies structured quality criteria that can be evaluated only after rendering. To address this problem, we introduce OmniManim, a render-feedback-aware educational animation generation framework built around a shared scene state, explicit visual planning, structured post-render diagnostics, and localized repair. Within OmniManim, the Vision Agent is a task-specific visual planning module: it predicts sparse keyframe layouts with coarse-to-fine bounding-box denoising and optimizes an interpolation-aware objective to reduce intermediate-frame failures induced by downstream animation interpolation. We further construct two datasets, ManimLayout-1K and EduRequire-500, and provide a reproducible evaluation protocol covering executability, instructional quality, visual quality, and efficiency. On EduRequire-500, OmniManim improves measured render quality over both single-model baselines and existing multi-agent frameworks. Systematic ablation studies further verify that explicit visual planning, especially its coarse spatial prior, bounding-box refinement, and interpolation-aware optimization, is central to these gains.

Programmatic video generation through code offers geometric precision and temporal coherence beyond pixel-level diffusion models, yet rigorously evaluating whether language models can produce spatially correct animated outputs remains an open problem. We introduce PRISM, a large-scale benchmark of 10,372 human-calibrated instruction-code pairs (20 times larger than prior programmatic video generation benchmarks), grounded in real-world knowledge visualization scenarios across English and Chinese and spanning 437 subject categories. We further propose a funnel-style evaluation framework with four complementary metrics: Code-Level Reliability for executability, Spatial Reasoning for layout correctness over full animation sequences, and Prompt-Aware Dynamic Visual Complexity (PADVC) and Temporal Density (TD) for diagnosing dynamic expression and temporal activity. Systematic evaluation of seven mainstream LLMs reveals a striking Execution-Spatial Gap: the average drop from execution success rate to spatial pass rate is approximately 41%, showing that runnable code does not necessarily yield spatially coherent visual output. These findings show that programmatic video generation evaluation should go beyond executability. PRISM provides a principled benchmark for advancing spatially coherent code generation.

Generating programmatic animation using libraries such as Manim presents unique challenges for Large Language Models (LLMs), requiring spatial reasoning, temporal sequencing, and familiarity with domain-specific APIs that are underrepresented in general pre-training data. A systematic study of how training and inference strategies interact in this setting is lacking in current research. This study introduces ManimTrainer, a training pipeline that combines Supervised Fine-tuning (SFT) with Reinforcement Learning (RL) based Group Relative Policy Optimisation (GRPO) using a unified reward signal that fuses code and visual assessment signals, and ManimAgent, an inference pipeline featuring Renderer-in-the-loop (RITL) and API documentation-augmented RITL (RITL-DOC) strategies. Using these techniques, this study presents the first unified training and inference study for text-to-code-to-video transformation with Manim. It evaluates 17 open-source sub-30B LLMs across nine combinations of training and inference strategies using ManimBench. Results show that SFT generally improves code quality, while GRPO enhances visual outputs and increases the models' responsiveness to extrinsic signals during self-correction at inference time. The Qwen 3 Coder 30B model with GRPO and RITL-DOC achieved the highest overall performance, with a 94% Render Success Rate (RSR) and 85.7% Visual Similarity (VS) to reference videos, surpassing the baseline GPT-4.1 model by +3 percentage points in VS. Additionally, the analysis shows that the correlation between code and visual metrics strengthens with SFT and GRPO but weakens with inference-time enhancements, highlighting the complementary roles of training and agentic inference strategies in Manim animation generation.