diff --git a/datafusion/core/tests/user_defined/mod.rs b/datafusion/core/tests/user_defined/mod.rs
index 4dad3ec4577d9..c2bc0ffa713af 100644
--- a/datafusion/core/tests/user_defined/mod.rs
+++ b/datafusion/core/tests/user_defined/mod.rs
@@ -45,3 +45,5 @@ mod insert_operation;
 /// Tests for `StatisticsRequest`s flowing from a custom optimizer rule
 /// through the physical planner into a custom `TableProvider`.
 mod statistics_requests;
+
+mod volatility;
diff --git a/datafusion/core/tests/user_defined/volatility.rs b/datafusion/core/tests/user_defined/volatility.rs
new file mode 100644
index 0000000000000..1e013ac1a5a6d
--- /dev/null
+++ b/datafusion/core/tests/user_defined/volatility.rs
@@ -0,0 +1,180 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+use std::sync::{
+    Arc,
+    atomic::{AtomicI64, Ordering},
+};
+
+use datafusion::arrow::array::{ArrayRef, AsArray};
+use datafusion::arrow::datatypes::{DataType, Field, FieldRef, Int64Type};
+use datafusion::common::test_util::batches_to_string;
+use datafusion::common::{Result, ScalarValue, assert_batches_eq};
+use datafusion::logical_expr::expr::{HigherOrderFunction, WindowFunction};
+use datafusion::logical_expr::{
+    ColumnarValue, Expr, HigherOrderFunctionArgs, HigherOrderReturnFieldArgs,
+    HigherOrderSignature, HigherOrderUDF, HigherOrderUDFImpl, LambdaParametersProgress,
+    PartitionEvaluator, ValueOrLambda, Volatility, col, create_udaf, create_udf,
+    create_udwf,
+};
+use datafusion::prelude::SessionContext;
+use datafusion_functions_aggregate::average::AvgAccumulator;
+
+static NEXT_VALUE: AtomicI64 = AtomicI64::new(0);
+
+#[derive(Debug, PartialEq, Eq, Hash)]
+struct NextValue {
+    signature: HigherOrderSignature,
+}
+
+impl HigherOrderUDFImpl for NextValue {
+    fn name(&self) -> &str {
+        "next_value"
+    }
+
+    fn signature(&self) -> &HigherOrderSignature {
+        &self.signature
+    }
+
+    fn lambda_parameters(
+        &self,
+        _step: usize,
+        _fields: &[ValueOrLambda<FieldRef, Option<FieldRef>>],
+    ) -> Result<LambdaParametersProgress> {
+        Ok(LambdaParametersProgress::Complete(vec![]))
+    }
+
+    fn return_field_from_args(
+        &self,
+        _args: HigherOrderReturnFieldArgs,
+    ) -> Result<FieldRef> {
+        Ok(Arc::new(Field::new("value", DataType::Int64, false)))
+    }
+
+    fn invoke_with_args(&self, _args: HigherOrderFunctionArgs) -> Result<ColumnarValue> {
+        let value = if self.signature.volatility == Volatility::Volatile {
+            NEXT_VALUE.fetch_add(1, Ordering::Relaxed)
+        } else {
+            0
+        };
+        Ok(ColumnarValue::Scalar(ScalarValue::Int64(Some(value))))
+    }
+}
+
+#[test]
+fn function_volatility() {
+    #[derive(Debug)]
+    struct IdentityEvaluator;
+
+    impl PartitionEvaluator for IdentityEvaluator {
+        fn evaluate_all(
+            &mut self,
+            values: &[ArrayRef],
+            _num_rows: usize,
+        ) -> Result<ArrayRef> {
+            Ok(Arc::clone(&values[0]))
+        }
+    }
+
+    for volatility in [
+        Volatility::Immutable,
+        Volatility::Stable,
+        Volatility::Volatile,
+    ] {
+        let scalar = create_udf(
+            "identity",
+            vec![DataType::Float64],
+            DataType::Float64,
+            volatility,
+            Arc::new(|args| Ok(args[0].clone())),
+        );
+        let aggregate = Arc::new(create_udaf(
+            "average",
+            vec![DataType::Float64],
+            Arc::new(DataType::Float64),
+            volatility,
+            Arc::new(|_| Ok(Box::<AvgAccumulator>::default())),
+            Arc::new(vec![DataType::UInt64, DataType::Float64]),
+        ));
+        let window = create_udwf(
+            "identity_window",
+            DataType::Float64,
+            Arc::new(DataType::Float64),
+            volatility,
+            Arc::new(|| Ok(Box::new(IdentityEvaluator))),
+        );
+        let higher_order = Arc::new(HigherOrderUDF::new_from_impl(NextValue {
+            signature: HigherOrderSignature::any(0, volatility),
+        }));
+
+        for expr in [
+            scalar.call(vec![col("value")]),
+            aggregate.call(vec![col("value")]),
+            WindowFunction::new(Arc::clone(&aggregate), vec![col("value")]).into(),
+            window.call(vec![col("value")]),
+            Expr::HigherOrderFunction(HigherOrderFunction::new(higher_order, vec![])),
+        ] {
+            let expected = volatility == Volatility::Volatile;
+            assert_eq!(expr.is_volatile_node(), expected, "{expr}");
+            assert_eq!(expr.is_volatile(), expected, "{expr}");
+            let aliased = expr.alias("result");
+            assert!(!aliased.is_volatile_node());
+            assert_eq!(aliased.is_volatile(), expected, "{aliased}");
+        }
+    }
+}
+
+#[tokio::test]
+async fn volatile_higher_order_function_is_not_eliminated() -> Result<()> {
+    let ctx = SessionContext::new();
+    ctx.register_higher_order_function(Arc::new(HigherOrderUDF::new_from_impl(
+        NextValue {
+            signature: HigherOrderSignature::any(0, Volatility::Volatile),
+        },
+    )));
+    let mut results = Vec::new();
+    let mut calls = Vec::new();
+    for sql in [
+        "SELECT next_value() AS first, next_value() AS second",
+        "SELECT next_value() = next_value() AS equal",
+    ] {
+        NEXT_VALUE.store(0, Ordering::Relaxed);
+        let batches = ctx.sql(sql).await?.collect().await?;
+        let count = NEXT_VALUE.load(Ordering::Relaxed);
+        println!("{sql}\n{}\ncalls={count}", batches_to_string(&batches));
+        results.push(batches);
+        calls.push(count);
+    }
+
+    let batch = &results[0][0];
+    assert_ne!(
+        batch.column(0).as_primitive::<Int64Type>().value(0),
+        batch.column(1).as_primitive::<Int64Type>().value(0)
+    );
+    assert_batches_eq!(
+        [
+            "+-------+",
+            "| equal |",
+            "+-------+",
+            "| false |",
+            "+-------+"
+        ],
+        &results[1]
+    );
+    assert_eq!(calls, vec![2, 2]);
+    Ok(())
+}
diff --git a/datafusion/expr/src/expr.rs b/datafusion/expr/src/expr.rs
index e8e805c2b9b75..c197a6af6fc40 100644
--- a/datafusion/expr/src/expr.rs
+++ b/datafusion/expr/src/expr.rs
@@ -2157,7 +2157,19 @@ impl Expr {
     /// - `rand()` returns `true`,
     /// - `a + rand()` returns `false`
     pub fn is_volatile_node(&self) -> bool {
-        matches!(self, Expr::ScalarFunction(func) if func.func.signature().volatility == Volatility::Volatile)
+        let volatility = match self {
+            Expr::ScalarFunction(func) => func.func.signature().volatility,
+            Expr::AggregateFunction(func) => func.func.signature().volatility,
+            Expr::WindowFunction(func) => match &func.fun {
+                WindowFunctionDefinition::AggregateUDF(func) => {
+                    func.signature().volatility
+                }
+                WindowFunctionDefinition::WindowUDF(func) => func.signature().volatility,
+            },
+            Expr::HigherOrderFunction(func) => func.func.signature().volatility,
+            _ => return false,
+        };
+        volatility == Volatility::Volatile
     }
 
     /// Returns true if the expression is volatile, i.e. whether it can return different