diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index b6adbd922..d13f5212b 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -3329,12 +3329,14 @@ static bool ggml_backend_cuda_device_supports_op(ggml_backend_dev_t dev, const g
                 return op->src[0]->ne[0] == 128 && op->src[0]->ne[1] % 16 == 0;
             } else {
                 // Mamba
-                // (kernel only supports d_state == 16, n_group == 1, d_head == 1)
-                return op->src[0]->ne[0] == 16 && op->src[4]->ne[1] == 1 && op->src[0]->ne[1] == 1;
+                // (kernel only supports d_state == 16, d_head == 1, n_head % 128 == 0, n_group == 1)
+                return op->src[0]->ne[0] == 16 && op->src[0]->ne[1] == 1 && op->src[0]->ne[2] % 128 == 0 && op->src[4]->ne[1] == 1;
             }
         }
-        case GGML_OP_SSM_CONV:
-            return true;
+        case GGML_OP_SSM_CONV: {
+            // assumes d_inner % threads == 0
+            return op->src[0]->ne[1] % 128 == 0;
+        }
         case GGML_OP_CONT:
             return op->src[0]->type != GGML_TYPE_BF16;
         case GGML_OP_DIAG_MASK_INF:
diff --git a/ggml/src/ggml-cuda/ssm-scan.cu b/ggml/src/ggml-cuda/ssm-scan.cu
index 61f35f859..dc3b1a9a8 100644
--- a/ggml/src/ggml-cuda/ssm-scan.cu
+++ b/ggml/src/ggml-cuda/ssm-scan.cu
@@ -204,7 +204,7 @@ static void ssm_scan_f32_cuda(const float * src0, const float * src1, const floa
     const int threads = 128;
     // NOTE: if you change conditions here, be sure to update the corresponding supports_op condition!
     if (src3_nb1 == sizeof(float)) {
-        // Mamba2
+        // Mamba-2
         if (d_state == 128) {
             GGML_ASSERT(d_state % threads == 0);
             // NOTE: can be any power of two between 4 and 64
@@ -219,8 +219,7 @@ static void ssm_scan_f32_cuda(const float * src0, const float * src1, const floa
             GGML_ABORT("doesn't support d_state!=128.");
         }
     } else {
-        // Mamba1
-        // todo: consider n_head cannot be divided, does this situation exist?
+        // Mamba-1
         GGML_ASSERT(n_head % threads == 0);
         GGML_ASSERT(head_dim == 1);
         GGML_ASSERT(n_group == 1);