diff --git a/.github/workflows/nightly-fuzz-test.yml b/.github/workflows/nightly-fuzz-test.yml
new file mode 100644
index 00000000000..2c05f711289
--- /dev/null
+++ b/.github/workflows/nightly-fuzz-test.yml
@@ -0,0 +1,37 @@
+name: Non-deterministic fuzz tests
+on:
+  workflow_dispatch:
+  schedule:
+    # Run nightly at 0300
+    - cron: "0 3 * * *"
+
+permissions:
+  contents: read
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+env:
+  # On regular PRs we run deterministic fuzzing to avoid flaky tests on CI.
+  # In the nightly tests we want to explore uncharted territory.
+  NOIR_AST_FUZZER_FORCE_NON_DETERMINISTIC: 1
+  # Tell arbtest how long it can run the tests for.
+  NOIR_AST_FUZZER_FORCE_BUDGET_SECS: 300
+
+jobs:
+  ast-fuzz:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Setup toolchain
+        uses: dtolnay/rust-toolchain@1.85.0
+        with:
+          targets: x86_64-unknown-linux-gnu
+
+      - name: Run tests
+        run: cargo test -p noir_ast_fuzzer_fuzz
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
\ No newline at end of file
diff --git a/tooling/ast_fuzzer/fuzz/src/lib.rs b/tooling/ast_fuzzer/fuzz/src/lib.rs
index 2ee78b57421..4fd77063757 100644
--- a/tooling/ast_fuzzer/fuzz/src/lib.rs
+++ b/tooling/ast_fuzzer/fuzz/src/lib.rs
@@ -16,13 +16,17 @@ use noirc_frontend::monomorphization::ast::Program;
 
 pub mod targets;
 
+fn bool_from_env(key: &str) -> bool {
+    std::env::var(key).map(|s| s == "1" || s == "true").unwrap_or_default()
+}
+
 // TODO(#7876): Allow specifying options on the command line.
 fn show_ast() -> bool {
-    std::env::var("NOIR_AST_FUZZER_SHOW_AST").map(|s| s == "1" || s == "true").unwrap_or_default()
+    bool_from_env("NOIR_AST_FUZZER_SHOW_AST")
 }
 
 fn show_ssa() -> bool {
-    std::env::var("NOIR_AST_FUZZER_SHOW_SSA").map(|s| s == "1" || s == "true").unwrap_or_default()
+    bool_from_env("NOIR_AST_FUZZER_SHOW_SSA")
 }
 
 pub fn default_ssa_options() -> SsaEvaluatorOptions {
diff --git a/tooling/ast_fuzzer/fuzz/src/targets/mod.rs b/tooling/ast_fuzzer/fuzz/src/targets/mod.rs
index 7d811c78852..0f57694748e 100644
--- a/tooling/ast_fuzzer/fuzz/src/targets/mod.rs
+++ b/tooling/ast_fuzzer/fuzz/src/targets/mod.rs
@@ -7,7 +7,7 @@ pub mod pass_vs_prev;
 #[cfg(test)]
 mod tests {
 
-    const TIMEOUT: Duration = Duration::from_secs(20);
+    const BUDGET: Duration = Duration::from_secs(20);
     const MIN_SIZE: u32 = 1 << 12;
     const MAX_SIZE: u32 = 1 << 20;
 
@@ -17,7 +17,9 @@ mod tests {
     use color_eyre::eyre;
     use proptest::prelude::*;
 
-    pub fn seed_from_env() -> Option<u64> {
+    use crate::bool_from_env;
+
+    fn seed_from_env() -> Option<u64> {
         let Ok(seed) = std::env::var("NOIR_ARBTEST_SEED") else { return None };
         let seed = u64::from_str_radix(seed.trim_start_matches("0x"), 16)
             .unwrap_or_else(|e| panic!("failed to parse seed '{seed}': {e}"));
@@ -25,10 +27,23 @@ mod tests {
     }
 
     /// Check if we are running on CI.
-    pub fn is_running_in_ci() -> bool {
+    fn is_running_in_ci() -> bool {
         std::env::var("CI").is_ok()
     }
 
+    /// Check if we explicitly want non-deterministic behavior, even on CI.
+    fn force_non_deterministic() -> bool {
+        bool_from_env("NOIR_AST_FUZZER_FORCE_NON_DETERMINISTIC")
+    }
+
+    /// How long to let non-deterministic tests run for.
+    fn budget() -> Duration {
+        std::env::var("NOIR_AST_FUZZER_BUDGET_SECS").ok().map_or(BUDGET, |b| {
+            let secs = b.parse().unwrap_or_else(|e| panic!("failed to parse budget; got {b}: {e}"));
+            Duration::from_secs(secs)
+        })
+    }
+
     /// `cargo fuzz` takes a long time to ramp up the complexity.
     /// This test catches crash bugs much faster.
     ///
@@ -46,7 +61,7 @@ mod tests {
 
         if let Some(seed) = seed_from_env() {
             run_reproduce(f, seed);
-        } else if is_running_in_ci() {
+        } else if is_running_in_ci() && !force_non_deterministic() {
             run_deterministic(f, cases);
         } else {
             run_nondeterministic(f);
@@ -73,7 +88,7 @@ mod tests {
         })
         .size_min(MIN_SIZE)
         .size_max(MAX_SIZE)
-        .budget(TIMEOUT)
+        .budget(budget())
         .run();
     }