Diagrams that reason before they draw
A picture is worth a thousand words only when the picture is right. Ask a general image model for a diagram of a triangle with a 90 degree angle, a labelled circuit, or the forces acting on a block on a slope, and you often get something that looks convincing but is quietly wrong: angles that do not add up, a resistor wired into a short, an arrow pointing the wrong way. Plausible is not the same as correct, and in a classroom the difference matters.
Project Lumina is ILM AI research into a different way of generating diagrams, one built specifically for teaching. It feeds directly into ilmino. The core idea is in the tagline: diagrams that reason before they draw. Instead of producing an image and hoping it is accurate, Lumina works out what must be true about a diagram first, then renders it to match.
The neuro-symbolic approach
The name neuro-symbolic describes two halves working together.
The neuro half is the neural image generator: diffusion and transformer models that have learned, from large volumes of visual material, how a clean mathematical or scientific diagram tends to look. This is what gives Lumina its fluency and its whiteboard style. On its own, though, a neural generator only knows what is typical. It has no grasp of whether a specific diagram is true.
The symbolic half supplies that missing knowledge as explicit rules:
- Geometry rules, so angles in a triangle sum to 180 degrees, a radius meets a tangent at a right angle, and parallel lines stay parallel.
- Physics laws, so force arrows have correct directions and relative magnitudes, ray diagrams obey reflection and refraction, and circuits form valid closed loops.
- Subject knowledge and syllabus definitions, so a labelled cell, a titration setup or a function graph matches how the topic is actually taught and assessed.
Lumina uses this symbolic layer to steer the neural generator. The rules constrain what the model is allowed to draw and are then used to check what it produced. The result is a diagram that is mathematically and scientifically correct by construction, rather than one that merely looks the part.
What Lumina can do
Text-to-sketch from a natural-language prompt
A teacher or student can describe what they need in plain language: "an isosceles triangle with the apex angle marked 40 degrees" or "a ray of light refracting as it enters a glass block". Lumina turns that prompt into a diagram. There is no need to learn drawing software, hunt for clip art or wrestle with an equation editor.
Symbolic verification for accuracy
Every diagram is checked against the relevant rules before it is shown. If the geometry does not hold or a physical relationship is violated, Lumina corrects it rather than passing the error on. This verification step is what separates a teaching tool from a novelty image generator, and it is why staff can trust what appears on screen.
Progressive rendering
Lumina can animate a diagram building step by step, the way a good teacher draws it out on the board: baseline first, then the triangle, then the labelled angle, then the construction lines. Learners see the order of construction, not just the finished object, which mirrors how the reasoning actually unfolds. It is the difference between watching a diagram be made and being handed one whole.
A clean whiteboard aesthetic
Diagrams share a consistent, uncluttered whiteboard style. That is a deliberate teaching choice: clear line weights, sensible labelling and no decorative noise, so attention stays on the concept.
Editable and annotatable output
Nothing Lumina produces is locked. Diagrams can be edited and annotated by both teachers and students. A teacher can adjust a label, extend a construction line or add a note before putting a diagram in front of a class. AI does the first draft; the teacher stays in control and can change anything.
Why this matters for institutions
Lumina is not a standalone toy. It changes what your platform can do in day-to-day teaching.
It turns Snap & Solve into a visual explanation
Until now, snapping a question returned a worked text answer. With Lumina, that same question can return a visual explanation: the diagram the answer depends on, built and labelled correctly, animated in the order a teacher would draw it. For geometry, mechanics, optics, graphs and countless other topics, the diagram is the explanation. Lumina supplies it.
Consistent, high-quality visual teaching across a department
Diagram quality usually varies from room to room and from one member of staff to the next. Lumina gives every teacher in a department access to the same accurate, well-labelled, consistently styled diagrams. Early-career teachers and non-specialists covering a class get the same visual standard as your most experienced staff. That consistency is hard to achieve any other way and it shows up directly in the quality of what learners see.
It reduces the time teachers spend drawing diagrams
Preparing accurate diagrams for slides, worksheets and the board is slow, and redrawing them for each variation is slower still. Generating a correct diagram from a sentence, then editing it, takes a fraction of the time. That is preparation time returned to teachers, and less of the marking-and-resource workload that drives so much of the working week.
Research that feeds the product
Project Lumina is ILM AI research, and it flows into ilmino rather than sitting in a lab. Grounding a neural generator in explicit subject knowledge is an active area of work, and we are candid about that: verification catches the cases where a purely neural model would drift, and teacher review remains the final check on everything that reaches a learner.
The full technical write-up, including how the symbolic layer is constructed and how verification works, is available on the ILM AI research site: Lumina: neuro-symbolic sketch synthesis.
What it means for your institution
- Correct by design. Diagrams are verified against geometry, physics and syllabus rules before anyone sees them, so what reaches your learners is accurate.
- Visual explanations at scale. Every worked answer can become a step-by-step visual one, across every classroom, without extra preparation.
- Consistency across staff. One high visual standard for the whole department, whoever is teaching.
- Time back for teachers. Less time drawing and redrawing diagrams, more time teaching.
- Staff stay in control. Every diagram is editable and annotatable, and teachers review before use.
If you would like to see Lumina inside ilmino and discuss what it could mean for your department, book a demo.
